{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"X\u00e9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x-ay=a \\\\ & ax+y=1 \\\\ \\end{align} \\right.$ . <br\/>Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang?","select":["<span class='basic_left'>A. V\u1edbi $a=5,$ h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t $(5;-12)$<\/span>","<span class='basic_left'>B. V\u1edbi m\u1ecdi $a,$ h\u1ec7 lu\u00f4n c\u00f3 nghi\u1ec7m duy nh\u1ea5t<\/span>","<span class='basic_left'>C. V\u1edbi m\u1ecdi $a \\ne \\pm 1$, h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t<\/span>"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> - Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi $a=5$ \u0111\u1ec3 ki\u1ec3m tra \u0111\u00e1p \u00e1n A<br\/>- T\u00ecm \u0111i\u1ec1u ki\u1ec7n c\u1ee7a $a$ \u0111\u1ec3 h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t \u0111\u1ec3 ki\u1ec3m tra \u0111\u00e1p \u00e1n B v\u00e0 C.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> + V\u1edbi $a=5,$ ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/span><br\/>$\\left\\{ \\begin{align} & x-5y=5 \\\\ & 5x+y=1 \\\\ \\end{align} \\right.$<br\/><span class='basic_left'>Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf, ta c\u00f3 <br\/>$\\left\\{ \\begin{align} & x=5y+5 \\\\ & 5\\left( 5y+5 \\right)+y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=5y+5 \\\\ & 26y=-24 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=5y+5 \\\\ & y=-\\dfrac{12}{13} \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=\\dfrac{5}{13} \\\\ & y=-\\dfrac{12}{13} \\\\ \\end{align} \\right.$ <br\/>Suy ra h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $\\left( \\dfrac{5}{13};-\\dfrac{12}{13} \\right)$ .<br\/> Do \u0111\u00f3 \u0111\u00e1p \u00e1n A sai<br\/>+ V\u1edbi $a=0,$ ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x=0 \\\\ & y=1 \\\\ \\end{align} \\right.$ .<br\/> Suy ra h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t<br\/>+ V\u1edbi $a$ kh\u00e1c $0,$ h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi $\\dfrac{1}{a}\\ne -\\dfrac{a}{1}\\Leftrightarrow {{a}^{2}}+1\\ne 0$ lu\u00f4n \u0111\u00fang v\u1edbi m\u1ecdi $a$<br\/>V\u1eady v\u1edbi m\u1ecdi $a,$ h\u1ec7 lu\u00f4n c\u00f3 nghi\u1ec7m duy nh\u1ea5t n\u00ean kh\u1eb3ng \u0111\u1ecbnh C sai v\u00e0 kh\u1eb3ng \u0111\u1ecbnh B \u0111\u00fang<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/>- \u0110\u1ed1i v\u1edbi c\u00e1c b\u00e0i to\u00e1n ch\u1ec9 \u0111o\u00e1n s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh th\u00ec ta n\u00ean d\u00f9ng c\u00e1ch x\u00e9t h\u1ec7 s\u1ed1 c\u1ee7a \u1ea9n d\u1ef1a theo v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng x\u00e1c \u0111\u1ecbnh b\u1edfi hai ph\u01b0\u01a1ng tr\u00ecnh trong h\u1ec7:<br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & ax+by=c \\\\ & a'x+b'y=c' \\\\ \\end{align} \\right.$ ($a,b,c,a\u2019,b\u2019,c\u2019$ kh\u00e1c $0$)<br\/>+ V\u00f4 nghi\u1ec7m n\u1ebfu $\\dfrac{a}{a'}=\\dfrac{b}{b'}\\ne \\dfrac{c}{c'}$<br\/> + V\u00f4 s\u1ed1 nghi\u1ec7m n\u1ebfu $\\dfrac{a}{a'}=\\dfrac{b}{b'}=\\dfrac{c}{c'}$<br\/>+ C\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t n\u1ebfu $\\dfrac{a}{a'}\\ne \\dfrac{b}{b'}$ <br\/>- \u0110\u1ed1i v\u1edbi b\u00e0i to\u00e1n t\u00ecm \u0111i\u1ec1u ki\u1ec7n c\u1ee7a tham s\u1ed1 \u0111\u1ec3 h\u1ec7 c\u00f3 nghi\u1ec7m th\u1ecfa m\u00e3n bi\u1ec3u th\u1ee9c c\u00f3 ch\u1ee9a nghi\u1ec7m: Ta bi\u1ebfn \u0111\u1ed5i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng quy t\u1eafc th\u1ebf ho\u1eb7c c\u1ed9ng \u0111\u1ea1i s\u1ed1. Khi \u0111\u00f3 ta thu \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh m\u00e0 trong \u0111\u00f3 c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n d\u1ea1ng $ax=b$ (*)<br\/>Khi \u0111\u00f3 s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd b\u1eb1ng s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (*)<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 nghi\u1ec7m duy nh\u1ea5t $\\Leftrightarrow a \\ne 0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m $\\Leftrightarrow a=b=0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) v\u00f4 nghi\u1ec7m n\u1ebfu $a=0$ v\u00e0 $b \\ne 0$<br\/><\/span>","column":1}]}],"id_ques":371},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>X\u00e9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x-ay=a \\\\ & ax+y=1 \\\\ \\end{align} \\right.$ v\u1edbi $a$ l\u00e0 tham s\u1ed1 . <br\/>T\u00ecm $a$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m th\u1ecfa m\u00e3n $x>0, y>0.$<\/span>","select":["A. $a=1$","B. $a>1$","C. $ 0 < a < 1 $"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: \u00c1p d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf, t\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 h\u1ec7 c\u00f3 nghi\u1ec7m. Sau \u0111\u00f3 t\u00ecm nghi\u1ec7m $(x;y)$ c\u1ee7a h\u1ec7 theo tham s\u1ed1 $a$<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i \u0111i\u1ec1u ki\u1ec7n $x>0,y>0$ \u0111\u1ec3 t\u00ecm $a.$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t c\u1ee7a h\u1ec7, bi\u1ec3u di\u1ec5n $x$ theo $y,$ ta \u0111\u01b0\u1ee3c $x=ay+a$ r\u1ed3i th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai, ta c\u00f3:<br\/>$ \\left\\{ \\begin{align} & x-ay=a \\\\ & ax+y=1 \\\\ \\end{align} \\right.$<br\/> $ \\Leftrightarrow \\left\\{ \\begin{align} & x=ay+a \\\\ & a\\left( ay+a \\right)+y=1 \\\\ \\end{align} \\right. $<br\/> $\\Leftrightarrow \\left\\{ \\begin{align} & x=ay+a \\\\ & {{a}^{2}}y+{{a}^{2}}+y=1 \\\\ \\end{align} \\right. $<br\/> $ \\Leftrightarrow \\left\\{ \\begin{align} & x=ay+a\\left( 1 \\right) \\\\ & \\left( {{a}^{2}}+1 \\right)y=1-{{a}^{2}}\\left( 2 \\right) \\\\ \\end{align} \\right.$<br\/>${{a}^{2}}+1\\ne 0$ v\u1edbi m\u1ecdi $a$ n\u00ean $\\left( 2 \\right)\\Leftrightarrow y=\\dfrac{1-{{a}^{2}}}{{{a}^{2}}+1}$ . <br\/>Thay $y=\\dfrac{1-{{a}^{2}}}{{{a}^{2}}+1}$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta c\u00f3 $x=\\dfrac{2a}{{{a}^{2}}+1}$ <br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $\\left( \\dfrac{2a}{{{a}^{2}}+1};\\dfrac{1-{{a}^{2}}}{{{a}^{2}}+1} \\right)$<br\/>Ta c\u00f3 $\\left\\{ \\begin{align} & x>0 \\\\ & y>0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & \\dfrac{2a}{{{a}^{2}}+1}>0 \\\\ & \\dfrac{1-{{a}^{2}}}{{{a}^{2}}+1}>0 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & 2a>0 \\\\ & 1-{{a}^{2}}>0 \\\\ \\end{align} \\right.$ (do ${{a}^{2}}+1>0$) <br\/>+ $ 2a >0 \\Leftrightarrow a > 0$ (3) <br\/>+ $1-{{a}^{2}}>0\\Leftrightarrow {{a}^{2}}<1\\Leftrightarrow \\left| a \\right|<1\\Leftrightarrow -1 < a < 1$ (4)<br\/>T\u1eeb (3) v\u00e0 (4), ta c\u00f3: $ 0 < a < 1 $ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m $x>0, y>0$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/> \u0110\u1ed1i v\u1edbi b\u00e0i to\u00e1n t\u00ecm \u0111i\u1ec1u ki\u1ec7n c\u1ee7a tham s\u1ed1 \u0111\u1ec3 h\u1ec7 c\u00f3 nghi\u1ec7m th\u1ecfa m\u00e3n bi\u1ec3u th\u1ee9c c\u00f3 ch\u1ee9a nghi\u1ec7m: Ta bi\u1ebfn \u0111\u1ed5i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng quy t\u1eafc th\u1ebf ho\u1eb7c c\u1ed9ng \u0111\u1ea1i s\u1ed1. Khi \u0111\u00f3 ta thu \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh m\u00e0 trong \u0111\u00f3 c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n d\u1ea1ng $ax=b$ (*)<br\/>Khi \u0111\u00f3 s\u1ed1 nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd b\u1eb1ng s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (*)<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 nghi\u1ec7m duy nh\u1ea5t $\\Leftrightarrow a \\ne 0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m $\\Leftrightarrow a=b=0$<br\/>+ Ph\u01b0\u01a1ng tr\u00ecnh (*) v\u00f4 nghi\u1ec7m n\u1ebfu $a=0$ v\u00e0 $b \\ne 0$<\/span><\/span>","column":3}]}],"id_ques":372},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"T\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a $a$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau t\u01b0\u01a1ng \u0111\u01b0\u01a1ng:<br\/>$\\left( I \\right)\\left\\{ \\begin{align} & 2x+3y=8 \\\\ & 3x-y=1 \\\\ \\end{align} \\right.$ v\u00e0 $\\left( II \\right)\\left\\{ \\begin{align} & ax-3y=-2 \\\\ & x+y=3 \\\\ \\end{align} \\right.$<br\/><b> \u0110\u00e1p s\u1ed1:<\/b> $a=$_input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng n\u1ebfu ch\u00fang cho chung t\u1eadp nghi\u1ec7m (*) <br\/>B\u01b0\u1edbc 1: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<br\/>B\u01b0\u1edbc 2: D\u00f9ng kh\u00e1i ni\u1ec7m (*) \u0111\u1ec3 t\u00ecm $a$<br\/>B\u01b0\u1edbc 3: Th\u1eed l\u1ea1i v\u1edbi $a$ v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c, h\u1ec7 (II) c\u00f3 chung t\u1eadp nghi\u1ec7m v\u1edbi h\u1ec7 (I) kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3:<br\/> $\\left( I \\right)\\Leftrightarrow\\left\\{ \\begin{align} & 2x+3y=8 \\\\ & 9x-3y=3 \\\\ \\end{align} \\right.$$\\Leftrightarrow\\left\\{ \\begin{align} & 2x+3y=8 \\\\ & 11x=11 \\\\ \\end{align} \\right.$ $\\Leftrightarrow\\left\\{ \\begin{align} & 2x+3y=8 \\\\ & x=1\\\\ \\end{align} \\right.$$\\Leftrightarrow\\left\\{ \\begin{align} & y=2 \\\\ & x=1 \\\\ \\end{align} \\right.$ <br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(1;2)$<br\/>\u0110\u1ec3 cho hai h\u1ec7 \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau th\u00ec nghi\u1ec7m $(1;2)$ ph\u1ea3i l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 (II). <br\/>Khi \u0111\u00f3, ta c\u00f3<br\/>$\\left\\{ \\begin{align} & a.1-3.2=-2 \\\\ & 1+2=3 \\\\ \\end{align} \\right.\\Leftrightarrow a=4$<br\/>Ng\u01b0\u1ee3c l\u1ea1i v\u1edbi $a=4$ th\u00ec h\u1ec7 (II) tr\u1edf th\u00e0nh $\\left\\{ \\begin{align} & 4x-3y=-2 \\\\ & x+y=3 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 4x-3y=-2 \\\\ & 3x+3y=9 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 7x=7 \\\\ & x+y=3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=1 \\\\ & y=2 \\\\ \\end{aligned} \\right.$ <br\/>V\u1eady v\u1edbi $a=4,$ h\u1ec7 (II) c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(1;2)$<br\/>Do \u0111\u00f3 v\u1edbi $a=4$ th\u00ec hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau.<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $4$<br\/><\/span><span class='basic_green'><b> L\u01b0u \u00fd: <\/b><\/span><br\/>H\u1ecdc sinh th\u01b0\u1eddng qu\u00ean kh\u00f4ng th\u1eed l\u1ea1i khi t\u00ecm \u0111\u01b0\u1ee3c $a.$<br\/> Trong tr\u01b0\u1eddng h\u1ee3p m\u1ed9t h\u1ec7 v\u00f4 s\u1ed1 nghi\u1ec7m, m\u1ed9t h\u1ec7 c\u00f3 nghi\u1ec7m duy nh\u1ea5t v\u1eabn c\u00f3 th\u1ec3 c\u00f3 chung 1 nghi\u1ec7m nh\u01b0ng kh\u00f4ng t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u00ec kh\u00f4ng c\u00f3 chung t\u1eadp nghi\u1ec7m<\/span>"}]}],"id_ques":373},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $a =-\\dfrac{3}{5}; b = \\dfrac{4}{5}$","B. $a =\\dfrac{3}{5}; b = \\dfrac{4}{5}$","C. $a =-\\dfrac{3}{5}; b = -\\dfrac{4}{5}$"],"ques":"T\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a $a,$ $b$ \u0111\u1ec3 hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau t\u01b0\u01a1ng \u0111\u01b0\u01a1ng:<br\/>$\\left( I \\right)\\left\\{ \\begin{align} & -2x+y=5 \\\\ & x+3y=1 \\\\ \\end{align} \\right.$ v\u00e0 $\\left( II \\right)\\left\\{ \\begin{align} & ax+by=2 \\\\ & bx+y=a \\\\ \\end{align} \\right.$ <br\/>","hint":"","explain":"<span class='basic_left'> Nh\u00e2n t\u1eebng v\u1ebf ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai c\u1ee7a h\u1ec7 (I) v\u1edbi $2,$ ta \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & -2x+y=5 \\\\ & 2x+6y=2 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & -2x+y=5 \\\\ & 7y=7 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & -2x+y=5 \\\\ & y=1 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x=-2 \\\\ & y=1 \\\\ \\end{align} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(-2;1)$<br\/>\u0110\u1ec3 cho hai h\u1ec7 \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau th\u00ec nghi\u1ec7m $(-2;1)$ ph\u1ea3i l\u00e0 nghi\u1ec7m c\u1ee7a h\u1ec7 (II). <br\/>Khi \u0111\u00f3, ta c\u00f3 $\\left\\{ \\begin{align} & a.\\left( -2 \\right)+b.1=2 \\\\ & b.\\left( -2 \\right)+1=a \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& -2a+b=2 \\\\ & a+2b=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & -4a+2b=4 \\\\ & a+2b=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 5a=-3 \\\\ & a+2b=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a=-\\dfrac{3}{5} \\\\ & b=\\dfrac{4}{5} \\\\ \\end{aligned} \\right.$<br\/>Ng\u01b0\u1ee3c l\u1ea1i v\u1edbi $\\left\\{ \\begin{aligned} & a=-\\dfrac{3}{5} \\\\ & b=\\dfrac{4}{5} \\\\ \\end{aligned} \\right.$ th\u00ec h\u1ec7 (II) tr\u1edf th\u00e0nh $\\left\\{ \\begin{aligned} & -\\dfrac{3}{5}x+\\dfrac{4}{5}y=2 \\\\ & \\dfrac{4}{5}x+y=-\\dfrac{3}{5} \\\\ \\end{aligned} \\right.$ <br\/>Gi\u1ea3i h\u1ec7 b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf: R\u00fat $y$ t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 2 c\u1ee7a h\u1ec7, ta t\u00ecm \u0111\u01b0\u1ee3c nghi\u1ec7m c\u1ee7a h\u1ec7 (II) l\u00e0 $(-2;1).$<br\/> Suy ra hai h\u1ec7 (II) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi h\u1ec7 (I)<br\/>V\u1eady v\u1edbi $a=-\\dfrac{3}{5};b=\\dfrac{4}{5}$ th\u00ec hai h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi nhau.<br\/><\/span>"}]}],"id_ques":374},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"X\u00e1c \u0111\u1ecbnh $m$ \u0111\u1ec3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau c\u00f3 nghi\u1ec7m duy nh\u1ea5t<br\/>$\\left\\{ \\begin{align} & 2x-y=1 \\\\ & x+y=2 \\\\ & mx-y=2m \\\\ \\end{align} \\right.$ <br\/><b> \u0110\u00e1p s\u1ed1:<\/b> $m=$_input_","hint":"","explain":"<span class='basic_left'> <span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: T\u1eeb hai ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea7u c\u1ee7a h\u1ec7, ta t\u00ecm nghi\u1ec7m $(x;y)$<br\/>B\u01b0\u1edbc 2: Thay $x,$ $y$ t\u00ecm \u0111\u01b0\u1ee3c v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 ba \u0111\u1ec3 t\u00ecm $m$<br\/>B\u01b0\u1edbc 3: Th\u1eed l\u1ea1i v\u1edbi $m$ v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t kh\u00f4ng?<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> X\u00e9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & 2x-y=1\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left( 1 \\right) \\\\ & x+y=2\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left( 2 \\right) \\\\ & mx-y=2m\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left( 3 \\right) \\\\ \\end{align} \\right.$<br\/>C\u1ed9ng v\u1ebf v\u1edbi v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00e0 (2) v\u1edbi nhau, ta \u0111\u01b0\u1ee3c: $3x=3\\Leftrightarrow x=1$ <br\/>Thay $x=1$ v\u00e0o (2), ta c\u00f3 $1+y=2\\Leftrightarrow y=1$<br\/>Thay $x=1; y=1$ v\u00e0o (3), ta c\u00f3: $m-1=2m\\Leftrightarrow m=-1$<br\/>V\u1edbi $m=-1,$ ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/>$\\left\\{ \\begin{aligned} & 2x-y=1 \\\\ & x+y=2 \\\\ & -x-y=-2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x-y=1 \\\\ & x+y=2 \\\\ \\end{aligned} \\right.$<br\/> H\u1ec7 n\u00e0y c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(1;1)$<br\/>V\u1eady v\u1edbi $m=-1$ th\u00ec h\u1ec7 \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$<\/span><\/span>"}]}],"id_ques":375},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{x+1}{y+2}=5 \\\\ & 3\\left( 2x-5 \\right)-4\\left( 3y+4 \\right)=5\\\\ \\end{align} \\right.$<br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0: ","select":["A. $(-1;4)$","B. $(-4;1)$","C. $(4;-1)$","D. $(1;-4)$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> B\u01b0\u1edbc 1: T\u00ecm \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh \u0111\u1ec3 m\u1eabu th\u1ee9c kh\u00e1c $0$<br\/> B\u01b0\u1edbc 2: \u0110\u01b0a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<br\/>B\u01b0\u1edbc 3: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c. So s\u00e1nh nghi\u1ec7m v\u1edbi \u0111i\u1ec1u ki\u1ec7n v\u00e0 k\u1ebft lu\u1eadn. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>\u0110i\u1ec1u ki\u1ec7n: $y \\ne -2$<br\/>$\\left\\{ \\begin{align} & \\dfrac{x+1}{y+2}=5 \\\\ & 3\\left( 2x-5 \\right)-4\\left( 3y+4 \\right)=5 \\\\ \\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x+1=5\\left( y+2 \\right) \\\\ & 6x-15-12y-16=5 \\\\ \\end{align} \\right. $$ \\Leftrightarrow \\left\\{ \\begin{align} & x-5y=9 \\\\ & 6x-12y=36 \\\\ \\end{align} \\right. $<br\/>$ \\Leftrightarrow \\left\\{ \\begin{align} & x-5y=9 \\\\ & x-2y=6 \\\\ \\end{align} \\right. $$\\Leftrightarrow\\begin{align} & \\left\\{ \\begin{aligned} & 3y=-3 \\\\ & x-2y=6 \\\\ \\end{aligned} \\right. \\Leftrightarrow \\left\\{ \\begin{aligned} & y=-1 \\\\ & x=2y+6 \\\\ \\end{aligned} \\right. \\\\ \\end{align}$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & y=-1 \\\\ & x=4 \\\\ \\end{align} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(4;-1)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":376},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["25"],["-18"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x+y=7 \\\\ & \\left( x+2 \\right)\\left( y+3 \\right)=xy+45 \\\\ \\end{align} \\right.$ <br\/> H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(x;y)=$(_input_;_input_) ","hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $ \\left\\{ \\begin{align} & x+y=7 \\\\ & \\left( x+2 \\right)\\left( y+3 \\right)=xy+45 \\\\ \\end{align} \\right.$ <br\/> $\\Leftrightarrow \\left\\{ \\begin{align} & x+y=7 \\\\ & xy+3x+2y+6=xy+45 \\\\ \\end{align} \\right.$<br\/>$ \\Leftrightarrow \\left\\{ \\begin{align} & x+y=7 \\\\ & 3x+2y=39 \\\\ \\end{align} \\right. $<br\/> $ \\Leftrightarrow \\left\\{ \\begin{align} & x=7-y \\\\ & 3\\left( 7-y \\right)+2y=39 \\\\ \\end{align} \\right. $<br\/>$ \\Leftrightarrow \\left\\{ \\begin{align} & x=7-y \\\\ & -y=18 \\\\ \\end{align} \\right.$<br\/>$ \\Leftrightarrow \\left\\{ \\begin{align} & x=25 \\\\ & y=-18 \\\\ \\end{align} \\right.$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(25;-18)$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o hai \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $25$ v\u00e0 $-18$ <\/span><\/span>"}]}],"id_ques":377},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & {{\\left( x-1 \\right)}^{2}}-{{\\left( x+2 \\right)}^{2}}=9y \\\\ & {{\\left( y-3 \\right)}^{2}}-{{\\left( y+2 \\right)}^{2}}=5x \\\\ \\end{align} \\right.$<br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0:","select":["A. $(5;3)$","B. $(-5;-3)$ ","C. $(5;-3)$ ","D. $(-5;3)$"],"hint":"S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ${{\\left( a\\pm b \\right)}^{2}}$ \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i v\u00e0 r\u00fat g\u1ecdn h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\begin{aligned} & \\left\\{ \\begin{aligned} & {{\\left( x-1 \\right)}^{2}}-{{\\left( x+2 \\right)}^{2}}=9y \\\\ & {{\\left( y-3 \\right)}^{2}}-{{\\left( y+2 \\right)}^{2}}=5x \\\\\\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & \\left( {{x}^{2}}-2x+1 \\right)-\\left( {{x}^{2}}+4x+4 \\right)=9y \\\\ & \\left( {{y}^{2}}-6y+9 \\right)-\\left( {{y}^{2}}+4y+4 \\right)=5x \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & 6x+9y=-3 \\\\ & 5x+10y=5 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & 2x+3y=-1 \\\\ & x+2y=1 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & 2\\left( 1-2y \\right)+3y=-1 \\\\ & x=1-2y \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & -y=-3 \\\\ & x=1-2y \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & y=3 \\\\ & x=-5 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(-5;3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span>","column":2}]}],"id_ques":378},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{1}{x-2}+\\dfrac{1}{y-1}=2 \\\\ & \\dfrac{2}{x-2}-\\dfrac{3}{y-1}=-1 \\\\ \\end{align} \\right.$ <br\/>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0","select":["A. $(3;2)$ ","B. $(2;3)$","C. $(1;2)$","D. $(2;1)$"],"hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t \u1ea9n ph\u1ee5","explain":"<span class='basic_left'>\u0110i\u1ec1u ki\u1ec7n: $ x\\ne 2$; $y\\ne 1$ <br\/>\u0110\u1eb7t $u=\\dfrac{1}{x-2},v=\\dfrac{1}{y-1}$ , ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><br\/> $\\left\\{ \\begin{align} & u+v=2 \\\\ & 2u-3v=-1 \\\\ \\end{align} \\right.$<span class='basic_left'>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, bi\u1ec3u di\u1ec5n $u$ theo $v$, ta \u0111\u01b0\u1ee3c: $u=2-v.$ <br\/> Th\u1ebf $u=2-v$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 2, ta \u0111\u01b0\u1ee3c:<br\/>$\\begin{aligned} & \\left\\{ \\begin{aligned} & u=2-v \\\\ & 2\\left( 2-v \\right)-3v=-1 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & u=2-v \\\\ & -5v=-5 \\\\ \\end{aligned} \\right. \\\\ & \\Leftrightarrow \\left\\{ \\begin{aligned} & u=1 \\\\ & v=1 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$<br\/> Suy ra $\\left\\{ \\begin{aligned} & \\dfrac{1}{x-2}=1 \\\\ & \\dfrac{1}{y-1}=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x-2=1 \\\\ & y-1=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=3 \\\\ & y=2 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(3;2)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":379},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $2x+3y=20$; $3x-5y=11$ v\u00e0 $x+y=9$ \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m, \u0111\u00fang hay sai? ","select":["A. \u0110\u00fang ","B. Sai"],"hint":"X\u00e9t xem h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp b\u1edfi ba ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a ba \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean c\u00f3 nghi\u1ec7m duy nh\u1ea5t kh\u00f4ng?","explain":"<span class='basic_left'>X\u00e9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/> $\\left\\{ \\begin{align} & 2x+3y=20\\,\\,\\left( 1 \\right) \\\\ & 3x-5y=11\\,\\,\\left( 2 \\right) \\\\ & x+y=9\\,\\,\\,\\,\\,\\,\\,\\,\\,\\left( 3 \\right) \\\\ \\end{align} \\right.$<br\/>$\\left( 3 \\right)\\Leftrightarrow x=9-y\\left( * \\right)$ <br\/>Th\u1ebf $x=9-y$ v\u00e0o (1), ta \u0111\u01b0\u1ee3c: $2\\left( 9-y \\right)+3y=20\\Leftrightarrow y=2$ <br\/>Th\u1ebf $x=9-y$ v\u00e0o (2), ta \u0111\u01b0\u1ee3c: $3\\left( 9-y \\right)-5y=11\\Leftrightarrow -8y=-16\\Leftrightarrow y=2$<br\/>Nh\u01b0 v\u1eady v\u1edbi $x=9-y,$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00e0 (2) \u0111\u1ec1u t\u00ecm \u0111\u01b0\u1ee3c $y=2$<br\/>Thay $y=2$ v\u00e0o (*), ta \u0111\u01b0\u1ee3c: $x=9-2=7$<br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $(7;2)$<br\/>Suy ra 3 \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 cho c\u00f9ng \u0111i qua \u0111i\u1ec3m $(7;2)$ hay ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":380},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $x =-\\dfrac{11}{5}; y = -\\dfrac{3}{5}$","B. $x =\\dfrac{11}{5}; y = -\\dfrac{3}{5}$","C. $x =-\\dfrac{11}{5}; y = \\dfrac{3}{5}$"],"ques":"<span class='basic_left'>T\u00ecm $x, y$ \u0111\u1ec3 bi\u1ec3u th\u1ee9c <br\/>$A={{\\left( x-2y+1 \\right)}^{2}}+{{\\left( 2x+y+5 \\right)}^{2}}$ \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t.","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: \u0110\u00e1nh gi\u00e1 bi\u1ec3u th\u1ee9c $A:$ N\u1ebfu $A\\ge m$ th\u00ec gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $m$<br\/>B\u01b0\u1edbc 2: T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $x$ \u0111\u1ec3 $A$ nh\u1ecf nh\u1ea5t. K\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: $\\left\\{ \\begin{align} & {{\\left( x-2y+1 \\right)}^{2}}\\ge 0 \\\\ & {{\\left( 2x+y+5 \\right)}^{2}}\\ge 0 \\\\ \\end{align} \\right.$ v\u1edbi m\u1ecdi $x;y$<br\/>Suy ra $A={{\\left( x-2y+1 \\right)}^{2}}+{{\\left( 2x+y+5 \\right)}^{2}}\\ge 0$ v\u1edbi m\u1ecdi $x;y$<br\/>Suy ra $\\min A=0$ <br\/>D\u1ea5u ''$=$'' x\u1ea3y ra $\\Leftrightarrow \\left\\{ \\begin{align} & {{\\left( x-2y+1 \\right)}^{2}}=0 \\\\ & {{\\left( 2x+y+5 \\right)}^{2}}=0 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x-2y+1=0 \\\\ & 2x+y+5=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x-2y=-1 \\\\ & 2x+y=-5 \\\\ \\end{aligned} \\right.\\left( * \\right)$<br\/>Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf, ta c\u00f3:<br\/>$\\left( * \\right)\\Leftrightarrow \\left\\{ \\begin{aligned} & x=2y-1 \\\\ & 2\\left( 2y-1 \\right)+y=-5 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=2y-1 \\\\ & 5y=-3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=-\\dfrac{11}{5} \\\\ & y=-\\dfrac{3}{5} \\\\ \\end{aligned} \\right.$ <br\/>V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $0$ \u0111\u1ea1t \u0111\u01b0\u1ee3c khi $\\left( x;y \\right)=\\left( -\\dfrac{11}{5};-\\dfrac{3}{5} \\right)$<br\/><\/span>."}]}],"id_ques":381},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & xy+2x=y \\\\ & xy+2y=x \\\\ \\end{align} \\right.$ c\u00f3 s\u1ed1 nghi\u1ec7m l\u00e0 ","select":["A.0","B. 1","C. 2","D. 3"],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3 <br\/>$\\left\\{ \\begin{align} & xy+2x=y\\left( 1 \\right) \\\\ & xy+2y=x\\left( 2 \\right) \\\\ \\end{align} \\right.$<br\/>Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7 cho nhau, ta \u0111\u01b0\u1ee3c<br\/>$\\left( xy+2x \\right)-\\left( xy+2y \\right)=y-x\\Leftrightarrow x=y$<br\/>Thay $x=y$ v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh (1), ta c\u00f3: <br\/>${{y}^{2}}+2y=y\\Leftrightarrow {{y}^{2}}+y=0\\Leftrightarrow y\\left( y+1 \\right)=0\\Leftrightarrow \\left[ \\begin{align} & y=0 \\\\ & y=-1 \\\\ \\end{align} \\right.$ <br\/>Suy ra $\\left[ \\begin{align} & x=y=0 \\\\ & x=y=-1 \\\\ \\end{align} \\right.$ <br\/>V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 hai nghi\u1ec7m l\u00e0 $(0;0)$ v\u00e0 $(-1;-1)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><br\/><span class='basic_green'><b>Nh\u1eadn x\u00e9t:<br\/><\/b> <\/span>H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh trong b\u00e0i to\u00e1n tr\u00ean l\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ed1i x\u1ee9ng lo\u1ea1i I: Khi ta thay \u0111\u1ed5i vai tr\u00f2 c\u1ee7a $x$ v\u00e0 $y$ cho nhau th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh kh\u00f4ng thay \u0111\u1ed5i<\/span>","column":4}]}],"id_ques":382},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-17"],["-24"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>\u0110a th\u1ee9c $P(x)$ chia h\u1ebft cho \u0111a th\u1ee9c $x-a$ khi v\u00e0 ch\u1ec9 khi $P(a) = 0$.<br\/>T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $m$ v\u00e0 $n$ sao cho \u0111a th\u1ee9c sau \u0111\u1ed3ng th\u1eddi chia h\u1ebft cho $x+1$ v\u00e0 $x+3$<br\/>$P\\left( x \\right)=m{{x}^{3}}+\\left( 2m-2 \\right){{x}^{2}}-\\left( 3n-5 \\right)x-4n$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $m=$_input_ v\u00e0 $n=$_input_<\/span>","hint":"","explain":"<span class='basic_left'>\u0110a th\u1ee9c $P(x)$ chia h\u1ebft cho $x+1$<br\/> $\\Leftrightarrow P\\left( -1 \\right)=0\\Leftrightarrow -m+\\left( 2m-2 \\right)+\\left( 3n-5 \\right)-4n=0$<br\/>$\\Leftrightarrow m-n=7$ (1)<br\/>\u0110a th\u1ee9c $P(x)$ chia h\u1ebft cho $x+3$<br\/> $\\Leftrightarrow P\\left( -3 \\right)=0\\Leftrightarrow -27m+9\\left( 2m-2 \\right)+3\\left( 3n-5 \\right)-4n=0$<br\/>$\\Leftrightarrow -9m+5n=33$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & m-n=7 \\\\ & 9m-5n=-33 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & m=n+7 \\\\ & 9\\left( n+7 \\right)-5n=-33 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & m=n+7 \\\\ & 4n=-96 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & m=-17 \\\\ & n=-24 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady $m=-17$, $n=-24$ th\u00ec th\u1ecfa m\u00e3n y\u00eau c\u1ea7u \u0111\u1ec1 b\u00e0i.<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $-17;-24$<\/span><\/span>"}]}],"id_ques":383},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t khu v\u01b0\u1eddn h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi $46$ $m.$ N\u1ebfu t\u0103ng chi\u1ec1u d\u00e0i $5$ $m$ v\u00e0 gi\u1ea3m chi\u1ec1u r\u1ed9ng $3$ $m$ th\u00ec chi\u1ec1u d\u00e0i g\u1ea5p $4$ l\u1ea7n chi\u1ec1u r\u1ed9ng. K\u00edch th\u01b0\u1edbc khu v\u01b0\u1eddn \u0111\u00f3 l\u00e0<\/span> ","select":["A. $8$ $m$ v\u00e0 $15$ $m$","B. $7$ $m$ v\u00e0 $16$ $m$","C. $9$ $m$ v\u00e0 $14$ $m$","D. $6$ $m$ v\u00e0 $17$ $m$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ G\u1ecdi \u1ea9n l\u00e0 c\u00e1c k\u00edch th\u01b0\u1edbc c\u1ee7a khu v\u01b0\u1eddn<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb chu vi c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb k\u00edch th\u01b0\u1edbc chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng t\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai.<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi chi\u1ec1u d\u00e0i khu v\u01b0\u1eddn l\u00e0 $x$ $(m)$ ; chi\u1ec1u r\u1ed9ng khu v\u01b0\u1eddn l\u00e0 $y$ $(m).$ \u0110i\u1ec1u ki\u1ec7n: $x>y>0$<br\/>V\u00ec chu vi khu v\u01b0\u1eddn l\u00e0 $46$ $m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $2(x+y)=46$ hay $x+y=23$ (1)<br\/>T\u0103ng chi\u1ec1u d\u00e0i $5$ $m$ th\u00ec chi\u1ec1u d\u00e0i l\u00e0 $x+5$ $(m)$ v\u00e0 gi\u1ea3m chi\u1ec1u r\u1ed9ng $3$ $m$ th\u00ec chi\u1ec1u r\u1ed9ng l\u00e0 $y-3$ $(m)$ <br\/>Do chi\u1ec1u d\u00e0i g\u1ea5p $4$ l\u1ea7n chi\u1ec1u r\u1ed9ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+5=4(y-3)$ hay $x-4y=-17$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/> $\\left\\{ \\begin{align} & x+y=23 \\\\ & x-4y=-17 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 5y=40 \\\\ & x-4y=-17 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=8 \\\\ & x=4y-17 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=8 \\\\ & x=15 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady chi\u1ec1u d\u00e0i khu v\u01b0\u1eddn l\u00e0 $15$ $m$ v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 $8$ $m.$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":384},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai \u0111\u1ed9i tr\u1ed3ng c\u00e2y g\u00e2y r\u1eebng trong th\u00e1ng tr\u01b0\u1edbc tr\u1ed3ng \u0111\u01b0\u1ee3c $700$ c\u00e2y. Trong th\u00e1ng n\u00e0y, \u0111\u1ed9i A v\u01b0\u1ee3t m\u1ee9c $60\\%$, \u0111\u1ed9i B v\u01b0\u1ee3t m\u1ee9c $40\\%.$ T\u00ednh xem m\u1ed7i \u0111\u1ed9i trong th\u00e1ng tr\u01b0\u1edbc tr\u1ed3ng \u0111\u01b0\u1ee3c bao nhi\u00eau c\u00e2y. Bi\u1ebft r\u1eb1ng trong th\u00e1ng n\u00e0y c\u1ea3 hai \u0111\u1ed9i tr\u1ed3ng \u0111\u01b0\u1ee3c $1100$ c\u00e2y.<br\/>S\u1ed1 c\u00e2y m\u00e0 \u0111\u1ed9i A v\u00e0 B tr\u1ed3ng \u0111\u01b0\u1ee3c trong th\u00e1ng tr\u01b0\u1edbc l\u1ea7n l\u01b0\u1ee3t l\u00e0","select":["A. $100$ c\u00e2y v\u00e0 $600$ c\u00e2y ","B. $600$ c\u00e2y v\u00e0 $100$ c\u00e2y","C. $500$ c\u00e2y v\u00e0 $200$ c\u00e2y"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>B\u1ea3ng ph\u00e2n t\u00edch k\u1ebft qu\u1ea3 tr\u1ed3ng c\u00e2y g\u00e2y r\u1eebng c\u1ee7a hai \u0111\u1ed9i A v\u00e0 B <br\/><table> <tr> <td>S\u1ed1 c\u00e2y<\/td> <td>\u0110\u1ed9i A<\/td> <td>\u0110\u1ed9i B <\/td> <td>T\u1ed5ng s\u1ed1 c\u00e2y<\/td> <\/tr> <tr> <td>Th\u00e1ng tr\u01b0\u1edbc<\/td> <td>$x$<\/td> <td>$y$<\/td> <td>$700$<\/td> <\/tr> <tr><td>Th\u00e1ng n\u00e0y<\/td><td>$x+60\\%x$<\/td><td>$y+40\\%y$<\/td> <td>$1100$<\/td><\/tr> <\/table><br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi $x$ l\u00e0 s\u1ed1 c\u00e2y \u0111\u1ed9i A tr\u1ed3ng \u0111\u01b0\u1ee3c trong th\u00e1ng tr\u01b0\u1edbc v\u00e0 $y$ l\u00e0 s\u1ed1 c\u00e2y \u0111\u1ed9i B tr\u1ed3ng \u0111\u01b0\u1ee3c trong th\u00e1ng tr\u01b0\u1edbc. \u0110i\u1ec1u ki\u1ec7n: $x,y$ nguy\u00ean d\u01b0\u01a1ng<br\/>V\u00ec hai \u0111\u1ed9i tr\u1ed3ng c\u00e2y g\u00e2y r\u1eebng trong th\u00e1ng tr\u01b0\u1edbc tr\u1ed3ng \u0111\u01b0\u1ee3c $700$ c\u00e2y n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=700$ (1)<br\/>Trong th\u00e1ng n\u00e0y, \u0111\u1ed9i A v\u01b0\u1ee3t m\u1ee9c $60\\%$ n\u00ean s\u1ed1 c\u00e2y \u0111\u1ed9i A tr\u1ed3ng \u0111\u01b0\u1ee3c l\u00e0 $x+\\dfrac{60}{100}x=1,6x$ (c\u00e2y); \u0111\u1ed9i B v\u01b0\u1ee3t m\u1ee9c $40\\%$ n\u00ean s\u1ed1 c\u00e2y \u0111\u1ed9i B tr\u1ed3ng \u0111\u01b0\u1ee3c l\u00e0 $y+\\dfrac{40}{100}y=1,4y$ (c\u00e2y). <br\/>Do trong th\u00e1ng n\u00e0y, c\u1ea3 hai \u0111\u1ed9i tr\u1ed3ng \u0111\u01b0\u1ee3c $1100$ c\u00e2y n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $1,6x+1,4y=1100$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x+y=700 \\\\ & 1,6x+1,4y=1100 \\\\ \\end{align} \\right.$ <br\/>$\\left\\{ \\begin{aligned} & x=700-y \\\\ & 1,6x+1,4y=1100 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=700-y \\\\ & 1,6\\left( 700-y \\right)+1,4y=1100 \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=700-y \\\\ & -0,2y=-20 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=600 \\\\ & y=100 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady th\u00e1ng tr\u01b0\u1edbc \u0111\u1ed9i A tr\u1ed3ng \u0111\u01b0\u1ee3c $600$ c\u00e2y, \u0111\u1ed9i B tr\u1ed3ng \u0111\u01b0\u1ee3c $100$ c\u00e2y.<br\/><span class='basic_left'><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":3}]}],"id_ques":385},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["24"],["3"]]],"list":[{"point":5,"width":150,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t ca n\u00f4 ch\u1ea1y xu\u00f4i d\u00f2ng s\u00f4ng \u0111\u01b0\u1ee3c $108$ $km$ r\u1ed3i ch\u1ea1y ng\u01b0\u1ee3c d\u00f2ng $63$ $km$ h\u1ebft t\u1ea5t c\u1ea3 $7$ gi\u1edd. M\u1ed9t l\u1ea7n kh\u00e1c, ca n\u00f4 n\u00e0y ch\u1ea1y xu\u00f4i d\u00f2ng $81$ $km$ r\u1ed3i ng\u01b0\u1ee3c d\u00f2ng $84$ $km$ c\u0169ng h\u1ebft $7$ gi\u1edd. H\u00e3y t\u00ednh v\u1eadn t\u1ed1c th\u1eadt c\u1ee7a ca n\u00f4 v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc.<br\/><b>\u0110\u00e1p s\u1ed1: <\/b>V\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 l\u00e0 _input_$km\/h$ v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 _input_$km\/h$<\/span> ","hint":"V\u1eadn t\u1ed1c xu\u00f4i d\u00f2ng $=$ v\u1eadn t\u1ed1c th\u1ef1c $+$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc; <br\/>V\u1eadn t\u1ed1c ng\u01b0\u1ee3c d\u00f2ng $=$ v\u1eadn t\u1ed1c th\u1ef1c $-$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ G\u1ecdi \u1ea9n l\u00e0 v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc. X\u00e1c \u0111\u1ecbnh v\u1eadn t\u1ed1c c\u1ee7a ca n\u00f4 khi xu\u00f4i d\u00f2ng v\u00e0 ng\u01b0\u1ee3c d\u00f2ng<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian c\u1ee7a ca n\u00f4 v\u1edbi t\u1eebng gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t \u1ea9n ph\u1ee5<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c ca n\u00f4 l\u00e0 $x$ $(km\/h),$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $y$ $(km\/h).$ \u0110i\u1ec1u ki\u1ec7n: $x>y>0$<br\/>V\u1eadn t\u1ed1c xu\u00f4i d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $x+y$ $(km\/h);$ v\u1eadn t\u1ed1c ng\u01b0\u1ee3c d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $x-y$ $(km\/h)$<br\/>M\u1ed9t ca n\u00f4 xu\u00f4i d\u00f2ng 1 d\u00f2ng s\u00f4ng d\u00e0i $108$ $km$ h\u1ebft $\\dfrac{108}{x+y}$ (h) v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng $63$ $km$ h\u1ebft $\\dfrac{63}{x-y}$ (h). <br\/>V\u00ec t\u1ed5ng th\u1eddi gian h\u1ebft $7$ gi\u1edd n\u00ean ta c\u00f3<\/span><br\/> $\\dfrac{108}{x+y}+\\dfrac{63}{x-y}=7$ (1)<br\/><span class='basic_left'>Ca n\u00f4 xu\u00f4i d\u00f2ng $81$ $km$ h\u1ebft $\\dfrac{81}{x+y}$ $(h)$ v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng $84$ $km$ h\u1ebft $\\dfrac{84}{x-y}$ $(h).$ V\u00ec t\u1ed5ng th\u1eddi gian h\u1ebft $7$ gi\u1edd n\u00ean ta c\u00f3<\/span><br\/> $\\dfrac{81}{x+y}+\\dfrac{84}{x-y}=7$ (2)<br\/><span class='basic_left'>T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/span> $\\left\\{ \\begin {align} & \\dfrac{108}{x+y}+\\dfrac{63}{x-y}=7 \\\\ & \\dfrac{81}{x+y}+\\dfrac{84}{x-y}=7 \\\\ \\end{align} \\right.$<br\/><span class='basic_left'>\u0110\u1eb7t $\\dfrac{1}{x+y}=u;\\dfrac{1}{x-y}=v$. <br\/>Ta c\u00f3 $\\left\\{ \\begin{align} & 108u+63v=7 \\\\ & 81u+84v=7 \\\\ \\end{align} \\right.$ <br\/>Gi\u1ea3i h\u1ec7 ta t\u00ecm \u0111\u01b0\u1ee3c $u=\\dfrac{1}{27};v=\\dfrac{1}{21}$<br\/> Suy ra $\\left\\{ \\begin{aligned} & x+y=27 \\\\ & x-y=21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x=48 \\\\ & y=x-21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=24 \\\\ & y=3 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 l\u00e0 $24$ $km\/h$ v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $3$ $km\/h$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $24$; $3.$<\/span><\/span>"}]}],"id_ques":386},{"time":24,"part":[{"time":3,"title":"Dung d\u1ecbch th\u1ee9 nh\u1ea5t ch\u1ee9a $30\\%$ axit HCl, dung d\u1ecbch th\u1ee9 hai ch\u01b0a $55\\%$ axit HCl. H\u1ecfi ph\u1ea3i tr\u1ed9n bao nhi\u00eau l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 nh\u1ea5t v\u1edbi dung d\u1ecbch lo\u1ea1i th\u1ee9 hai \u0111\u1ec3 \u0111\u01b0\u1ee3c $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\% $ axit HCl.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[6],[1],[5],[4],[3]]],"list":[{"point":5,"image":"img\/1.png","left":["L\u01b0\u1ee3ng axit HCl c\u00f3 trong dung d\u1ecbch th\u1ee9 nh\u1ea5t l\u00e0 $30\\%x$ (l\u00edt). L\u01b0\u1ee3ng axit HCl c\u00f3 trong dung d\u1ecbch th\u1ee9 hai l\u00e0 $55\\%y$ (l\u00edt). L\u01b0\u1ee3ng axit HCl c\u00f3 trong $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl l\u00e0 $50\\%.100=50$ (l\u00edt). Theo \u0111\u1ec1 ra, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $30\\%x+55\\%y=50$ (1)","V\u1eady c\u1ea7n tr\u1ed9n $20$ l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 nh\u1ea5t v\u1edbi $80$ l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 hai \u0111\u1ec3 \u0111\u01b0\u1ee3c $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl. ","G\u1ecdi $x$ l\u00e0 s\u1ed1 l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 nh\u1ea5t v\u00e0 $y$ l\u00e0 s\u1ed1 l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 hai c\u1ea7n tr\u1ed9n \u0111\u1ec3 \u0111\u01b0\u1ee3c $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl. \u0110i\u1ec1u ki\u1ec7n: $ 0 < x, y <100$ ","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $x=20$ v\u00e0 $y=80$ (th\u1ecfa m\u00e3n)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & x+y=100 \\\\ & 30\\%x+55\\%y=50 \\\\ \\end{align} \\right.$","Do t\u1ed5ng s\u1ed1 l\u00edt l\u00e0 $100$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x+y=100$ (2)"],"top":120,"hint":"","explain":"<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 nh\u1ea5t v\u00e0 $y$ l\u00e0 s\u1ed1 l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 hai c\u1ea7n tr\u1ed9n \u0111\u1ec3 \u0111\u01b0\u1ee3c $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl. \u0110i\u1ec1u ki\u1ec7n: $ 0 < x, y <100$<br\/>L\u01b0\u1ee3ng axit HCl c\u00f3 trong dung d\u1ecbch th\u1ee9 nh\u1ea5t l\u00e0 $30\\%x$ (l\u00edt).<br\/> L\u01b0\u1ee3ng axit HCl c\u00f3 trong dung d\u1ecbch th\u1ee9 hai l\u00e0 $55\\%y$ (l\u00edt).<br\/> L\u01b0\u1ee3ng axit HCl c\u00f3 trong $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl l\u00e0 $50\\%.100=50$(l\u00edt).<br\/>Theo \u0111\u1ec1 ra, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $30\\%x+55\\%y=50$ (1)<br\/>Do t\u1ed5ng s\u1ed1 l\u00edt l\u00e0 $100$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x+y=100$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & x+y=100 \\\\ & 30\\%x+55\\%y=50 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow\\left\\{ \\begin{align} & x+y=100 \\\\ & \\dfrac{30}{100}x+\\dfrac{55}{100}y=50 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{aligned} & x+y=100 \\\\ & 6x+11y=1000 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=100-y \\\\ & 6\\left( 100-y \\right)+11y=1000 \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=100-y \\\\ & 5y=400 \\\\ \\end{aligned} \\right.$$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=100-y \\\\ & y=80 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=20 \\\\ & y=80 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady c\u1ea7n tr\u1ed9n $20$ l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 nh\u1ea5t v\u1edbi $80$ l\u00edt dung d\u1ecbch lo\u1ea1i th\u1ee9 hai \u0111\u1ec3 \u0111\u01b0\u1ee3c $100$ l\u00edt dung d\u1ecbch ch\u1ee9a $50\\%$ axit HCl.<\/span>"}]}],"id_ques":387},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["21"],["28"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Hai v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o m\u1ed9t b\u1ec3 n\u01b0\u1edbc c\u1ea1n th\u00ec sau $12$ gi\u1edd b\u1ec3 \u0111\u1ea7y. Ng\u01b0\u1eddi ta m\u1edf c\u1ea3 hai v\u00f2i trong $4$ gi\u1edd th\u00ec kh\u00f3a v\u00f2i II l\u1ea1i v\u00e0 \u0111\u1ec3 v\u00f2i I ch\u1ea3y ti\u1ebfp $14$ gi\u1edd n\u1eefa m\u1edbi \u0111\u1ea7y b\u1ec3. H\u1ecfi n\u1ebfu m\u1ed7i v\u00f2i ch\u1ea3y ri\u00eang th\u00ec sau bao l\u00e2u m\u1edbi \u0111\u1ea7y b\u1ec3? <br\/><b> \u0110\u00e1p s\u1ed1: <\/b>Th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_gi\u1edd<br\/> Th\u1eddi gian v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_gi\u1edd<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>+ G\u1ecdi \u1ea9n l\u00e0 th\u1eddi gian m\u1ed7i v\u00f2i ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/>+ T\u1eeb gi\u1ea3i thi\u1ebft hai v\u00f2i c\u00f9ng ch\u1ea3y th\u00ec sau $12$ gi\u1edd \u0111\u1ea7y b\u1ec3, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb trong $1$ gi\u1edd, s\u1ed1 ph\u1ea7n b\u1ec3 hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c<br\/>+ T\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai, ta t\u00ednh xem t\u1eeb l\u00fac kh\u00f3a v\u00f2i II th\u00ec v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c bao nhi\u00eau ph\u1ea7n b\u1ec3 r\u1ed3i t\u1eeb \u0111\u00f3 thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh. <br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m c\u00f3 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi $x$ gi\u1edd l\u00e0 th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3; $y$ gi\u1edd l\u00e0 th\u1eddi gian v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/> \u0110i\u1ec1u ki\u1ec7n $ x>0,y>0$<br\/>Trong $1$ gi\u1edd v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ b\u1ec3, v\u00f2i II ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$ b\u1ec3<br\/>Do 2 v\u00f2i ch\u1ea3y $12$ gi\u1edd th\u00ec \u0111\u1ea7y b\u1ec3 n\u00ean trong $1$ gi\u1edd, hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{12}$ b\u1ec3 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12}$ (1)<br\/>Hai v\u00f2i ch\u1ea3y trong $4$ gi\u1edd th\u00ec \u0111\u01b0\u1ee3c $\\dfrac{4}{12}=\\dfrac{1}{3}$ b\u1ec3. Sau \u0111\u00f3 kh\u00f3a v\u00f2i II v\u00e0 v\u00f2i I ch\u1ea3y ti\u1ebfp trong $14$ gi\u1edd n\u1eefa m\u1edbi \u0111\u1ea7y b\u1ec3 n\u00ean v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c th\u00eam $\\dfrac{14}{x}$ ph\u1ea7n b\u1ec3.<br\/>V\u00ec s\u1ed1 ph\u1ea7n b\u1ec3 c\u00f2n l\u1ea1i sau khi kh\u00f3a v\u00f2i II l\u00e0 $1-\\dfrac{1}{3}=\\dfrac{2}{3}$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:$\\dfrac{14}{x}=\\dfrac{2}{3}$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12} \\\\ & \\dfrac{14}{x}=\\dfrac{2}{3} \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12} \\\\ & x=21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{y}+\\dfrac{1}{21}=\\dfrac{1}{12} \\\\ & x=21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=21 \\\\ & y=28 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n). <br\/>V\u1eady v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 trong $21$ gi\u1edd, v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 trong $28$ gi\u1edd.<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $21$ v\u00e0 $28$<\/span><\/span>"}]}],"id_ques":388},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai n\u0103m tr\u01b0\u1edbc \u0111\u00e2y tu\u1ed5i anh g\u1ea5p \u0111\u00f4i tu\u1ed5i c\u1ee7a em, c\u00f2n $8$ n\u0103m tr\u01b0\u1edbc \u0111\u00e2y, tu\u1ed5i anh g\u1ea5p $5$ l\u1ea7n tu\u1ed5i em. H\u1ecfi hi\u1ec7n nay, anh v\u00e0 em bao nhi\u00eau tu\u1ed5i? <\/span>","select":["A. Hi\u1ec7n nay, em $12$ tu\u1ed5i, anh $18$ tu\u1ed5i ","B. Hi\u1ec7n nay, em $12$ tu\u1ed5i, anh $17$ tu\u1ed5i ","C. Hi\u1ec7n nay, em $11$ tu\u1ed5i, anh $18$ tu\u1ed5i","D. Hi\u1ec7n nay, em $10$ tu\u1ed5i, anh $18$ tu\u1ed5i "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>+ Ch\u1ecdn \u1ea9n l\u00e0 tu\u1ed5i anh v\u00e0 tu\u1ed5i em hi\u1ec7n nay. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n.<br\/>+ Thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb cho tu\u1ed5i anh v\u00e0 tu\u1ed5i em hai n\u0103m tr\u01b0\u1edbc<br\/>+Thi\u1ebft l\u1eadp bi\u1ec3u th\u1ee9c tu\u1ed5i anh v\u00e0 em hai n\u0103m sau<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi tu\u1ed5i anh hi\u1ec7n nay l\u00e0 $x$ (tu\u1ed5i), tu\u1ed5i em hi\u1ec7n nay l\u00e0 $y$ (tu\u1ed5i). \u0110i\u1ec1u ki\u1ec7n $x>y>8$<br\/>Hai n\u0103m tr\u01b0\u1edbc, tu\u1ed5i anh l\u00e0 $x-2$ (tu\u1ed5i), tu\u1ed5i em l\u00e0 $y-2$ (tu\u1ed5i).<br\/> V\u00ec hai n\u0103m tr\u01b0\u1edbc \u0111\u00e2y tu\u1ed5i anh g\u1ea5p \u0111\u00f4i tu\u1ed5i c\u1ee7a em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x-2=2(y-2)$ (1)<br\/>T\u00e1m n\u0103m tr\u01b0\u1edbc, tu\u1ed5i anh l\u00e0 $x-8$ (tu\u1ed5i), tu\u1ed5i em l\u00e0 $y-8$(tu\u1ed5i).<br\/> V\u00ec $8$ n\u0103m tr\u01b0\u1edbc \u0111\u00e2y, tu\u1ed5i anh g\u1ea5p 5 l\u1ea7n tu\u1ed5i em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh $x-8=5(y-8)$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & x-2=2\\left( y-2 \\right) \\\\ & x-8=5\\left( y-8 \\right) \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{align} & x-2y=-2 \\\\ & x-5y=-32 \\\\ \\end{align} \\right.$ $\\Leftrightarrow \\left\\{ \\begin{aligned} & 3y=30 \\\\ & x-5y=-32 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=10 \\\\ & x=18 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady hi\u1ec7n nay, anh $18$ tu\u1ed5i, em $10$ tu\u1ed5i.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":389},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Hai ng\u01b0\u1eddi kh\u00e1ch \u0111i du l\u1ecbch xu\u1ea5t ph\u00e1t \u0111\u1ed3ng th\u1eddi t\u1eeb hai th\u00e0nh ph\u1ed1 c\u00e1ch nhau $40$ $km$. H\u1ecd \u0111i ng\u01b0\u1ee3c chi\u1ec1u v\u00e0 g\u1eb7p nhau sau $4$ gi\u1edd. H\u1ecfi v\u1eadn t\u1ed1c c\u1ee7a m\u1ed7i ng\u01b0\u1eddi bi\u1ebft r\u1eb1ng \u0111\u1ebfn khi g\u1eb7p nhau, ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i nhi\u1ec1u h\u01a1n ng\u01b0\u1eddi th\u1ee9 hai $8$ $km.$ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b>V\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 _input_$(km\/h)$, v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 _input_$(km\/h)$<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u1ea3ng ph\u00e2n t\u00edch chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a hai ng\u01b0\u1eddi kh\u00e1ch<br\/><table> <tr> <td><\/td> <td>V\u1eadn t\u1ed1c $(km\/h)$<\/td> <td>Th\u1eddi gian $(h)$<\/td> <td>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<\/td> <\/tr> <tr> <td>Ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t<\/td> <td>$x$<\/td> <td>$4$<\/td> <td>$4x$<\/td> <\/tr> <tr><td>Ng\u01b0\u1eddi th\u1ee9 hai<\/td><td>$y$<\/td><td>$4$<\/td> <td>$4y$<\/td><\/tr> <\/table> <br\/><b>Ch\u00fa \u00fd:<\/b> Chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a hai ng\u01b0\u1eddi l\u00e0 ng\u01b0\u1ee3c chi\u1ec1u n\u00ean t\u1ed5ng qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a hai ng\u01b0\u1eddi \u0111\u1ebfn khi g\u1eb7p nhau ch\u00ednh l\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa hai th\u00e0nh ph\u1ed1<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 nh\u1ea5t l\u00e0 $x$ $(km\/h);$ v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 hai l\u00e0 $y$ $(km\/h).$ \u0110i\u1ec1u ki\u1ec7n: $x,y>0$<br\/>Th\u1eddi gian \u0111i \u0111\u01b0\u1ee3c c\u1ee7a hai ng\u01b0\u1eddi kh\u00e1ch l\u00e0 $4$ gi\u1edd n\u00ean ta c\u00f3 qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 nh\u1ea5t l\u00e0 $4x$ $(km)$ v\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 hai l\u00e0 $4y$ $(km)$<br\/>Do hai ng\u01b0\u1eddi \u0111i ng\u01b0\u1ee3c chi\u1ec1u nhau n\u00ean khi g\u1eb7p nhau, t\u1ed5ng qu\u00e3ng \u0111\u01b0\u1eddng hai ng\u01b0\u1eddi kh\u00e1ch \u0111i \u0111\u01b0\u1ee3c b\u1eb1ng v\u1edbi kho\u1ea3ng c\u00e1ch gi\u1eefa hai th\u00e0nh ph\u1ed1.<br\/> Do \u0111\u00f3, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $4x+4y=40$ (1)<br\/>V\u00ec khi g\u1eb7p nhau, ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i nhi\u1ec1u h\u01a1n ng\u01b0\u1eddi th\u1ee9 hai $8$ $km$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $4x-4y=8$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & 4x+4y=40 \\\\ & 4x-4y=8 \\\\ \\end{align} \\right.$<br\/> $\\Leftrightarrow \\left\\{ \\begin{aligned} & 8x=48 \\\\ & 4x-4y=8 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=6 \\\\ & 4y=16 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=6 \\\\ & y=4 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 nh\u1ea5t l\u00e0 $6$ $(km\/h);$ v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi kh\u00e1ch th\u1ee9 hai l\u00e0 $4$ $(km\/h).$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $6$ v\u00e0 $4$<\/span><\/span>"}]}],"id_ques":390}],"lesson":{"save":0,"level":2}}