{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $x^2 - 4|x| - 5 = 0$","select":[" $S = \\left\\{-5; 5\\right\\}$"," $S = \\left\\{-3; 3\\right\\}$","$S = \\left\\{-3; -5\\right\\}$","$S = \\left\\{3; 5\\right\\}$"],"hint":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>+ V\u1edbi $x \\geq 0$ th\u00ec:<br\/>$x^2 - 4|x|- 5 = 0$ <br\/>$\\Leftrightarrow x^2 - 4x - 5 = 0$<br\/>$\\Leftrightarrow x^2 + x - 5x - 5 = 0$<br\/>$\\Leftrightarrow x(x + 1) - 5(x + 1) = 0$<br\/>$\\Leftrightarrow (x + 1)(x - 5) = 0$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x + 1 = 0\\\\ x - 5 = 0\\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x = -1 \\hspace{0,2cm} \\text{(lo\u1ea1i)} \\\\ x = 5 \\hspace{0,2cm} \\text{(nh\u1eadn)} \\end{array} \\right.$<br\/>+ V\u1edbi $x < 0$ th\u00ec: <br\/>$x^2 - 4|x| - 5 = 0$ <br\/>$\\Leftrightarrow x^2 + 4x - 5 = 0$<br\/>$\\Leftrightarrow x^2 -x + 5x - 5 = 0$<br\/>$\\Leftrightarrow x(x - 1) + 5(x - 1) = 0$<br\/>$\\Leftrightarrow (x - 1)(x + 5) = 0$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x - 1 = 0\\\\ x + 5 = 0\\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x = 1 \\hspace{0,2cm} \\text{(lo\u1ea1i)} \\\\ x = -5 \\hspace{0,2cm} \\text{(nh\u1eadn)} \\end{array} \\right.$ <br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 t\u1eadp nghi\u1ec7m l\u00e0 $S = \\left\\{-5; 5\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{-5; 5\\right\\}$<\/span><\/span> ","column":2}]}],"id_ques":1241},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $\\left| x + \\dfrac{1}{1.5}\\right| + \\left| x + \\dfrac{1}{5.9}\\right| + ... + \\left| x + \\dfrac{1}{397.401}\\right| = 101x$ ","select":[" A. Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m"," B. $S = \\varnothing $","C. $x = \\dfrac{400}{401}$","D. $x = \\dfrac{100}{401}$"],"hint":"","explain":"<span class='basic_left'>Nh\u1eadn th\u1ea5y v\u1ebf tr\u00e1i kh\u00f4ng \u00e2m v\u1edbi m\u1ecdi $x$ n\u00ean \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 $x$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 v\u1ebf ph\u1ea3i kh\u00f4ng \u00e2m, t\u1ee9c l\u00e0: $101x \\geq 0 \\Leftrightarrow x \\geq 0$<br\/>Khi \u0111\u00f3 c\u00e1c bi\u1ec3u th\u1ee9c trong t\u1ea5t c\u1ea3 c\u00e1c d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u1edf v\u1ebf tr\u00e1i \u0111\u1ec1u d\u01b0\u01a1ng.<br\/>V\u00ec v\u1eady ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh:<br\/>$\\left( x + \\dfrac{1}{1.5}\\right) + \\left( x + \\dfrac{1}{5.9}\\right) + ... + \\left( x + \\dfrac{1}{397.401}\\right) = 101x$<br\/> $\\Leftrightarrow \\left( \\dfrac{1}{1.5} + \\dfrac{1}{5.9} + ... + \\dfrac{1}{397.401}\\right) + 100x = 101x$<br\/>$\\Leftrightarrow x = \\dfrac{1}{1.5} + \\dfrac{1}{5.9} + ... + \\dfrac{1}{397.401}$<br\/>$\\Leftrightarrow 4x = \\dfrac{4}{1.5} + \\dfrac{4}{5.9} + ... + \\dfrac{4}{397.401}$<br\/>$\\Leftrightarrow 4x = 1- \\dfrac{1}{5} + \\dfrac{1}{5} - \\dfrac{1}{9} + \\dfrac{1}{9 } - ... + \\dfrac{1}{397} - \\dfrac{1}{401}$<br\/>$\\Leftrightarrow 4x = 1 - \\dfrac{1}{401}$<br\/>$\\Leftrightarrow 4x = \\dfrac{400}{401}$ <br\/>$\\Leftrightarrow x = \\dfrac{100}{401}$ (th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n $x \\geq 0$)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m l\u00e0 $x = \\dfrac{100}{401}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span> ","column":2}]}],"id_ques":1242},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|3x - 7| \\leq |2x + 5|$ ","select":[" A. $\\dfrac{2}{5} \\leq x \\leq 12$"," B. $\\dfrac{-2}{5} \\leq x \\leq 12$","C. $x \\leq \\dfrac{2}{5}$ ho\u1eb7c $x \\leq 12 $","D. $x \\geq \\dfrac{2}{5}$ ho\u1eb7c $x \\geq 12$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>$|A| \\leq |B| \\Leftrightarrow A^2 \\leq B^2 \\Leftrightarrow A^2 - B^2 \\leq 0 \\Leftrightarrow (A-B)(A +B) \\leq 0$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$|3x - 7| \\leq |2x + 5|$<br\/>$\\Leftrightarrow (3x - 7)^2 \\leq (2x + 5)^2$<br\/>$\\Leftrightarrow (3x - 7)^2 - (2x + 5)^2 \\leq 0$<br\/>$\\Leftrightarrow (3x -7 - 2x - 5)(3x - 7 + 2x + 5) \\leq 0$<br\/>$\\Leftrightarrow (x - 12)(5x - 2) \\leq 0$<br\/><b> Tr\u01b0\u1eddng h\u1ee3p $1$:<\/b><br\/>$\\left\\{\\begin{array}{l} x - 12 \\leq 0\\\\ 5x - 2 \\geq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\leq 12\\\\ x \\geq \\dfrac{2}{5} \\end{array} \\right.$ $\\Leftrightarrow$ $\\dfrac{2}{5} \\leq x \\leq 12$<br\/><b>Tr\u01b0\u1eddng h\u1ee3p $2$:<\/b><br\/>$\\left\\{\\begin{array}{l} x - 12 \\geq 0\\\\ 5x - 2 \\leq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\geq 12 \\\\ x \\leq \\dfrac{2}{5} \\end{array} \\right.$ (lo\u1ea1i)<br\/>V\u1eady nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $\\dfrac{2}{5} \\leq x \\leq 12$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span> <\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1243},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/7.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $2||x + 1| - 5| = 24$ ","select":[" $S = \\left\\{-18 \\right\\}$"," $S = \\left\\{-16; 18 \\right\\}$","$S = \\left\\{-18; 16 \\right\\}$","$S = \\left\\{-18; -16 \\right\\}$"],"hint":"B\u1ecf t\u1eebng gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>$2||x + 1| - 5| = 24$ $\\Leftrightarrow$ $||x + 1| - 5| = 12$ $\\Leftrightarrow$ $\\left[\\begin{array}{l} |x + 1| - 5 = 12\\\\ |x + 1| - 5 = -12 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left[\\begin{array}{l} |x + 1| = 17 \\hspace{0,2cm} (1) \\\\ |x + 1| = -7 \\text{(lo\u1ea1i)} \\end{array} \\right.$<br\/> $(1) \\Leftrightarrow \\left[\\begin{array}{l} x + 1 = 17 \\hspace{0,2cm} \\text{n\u1ebfu} \\hspace{0,2cm} x \\geq -1 \\\\ x + 1 = -17 \\hspace{0,2cm} \\text{n\u1ebfu} \\hspace{0,2cm} x < -1 \\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 16 \\text{(nh\u1eadn)} \\\\ x = -18 \\text{(nh\u1eadn)} \\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{-18; 16 \\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{-18; 16 \\right\\}$<\/span><\/span> ","column":2}]}],"id_ques":1244},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/3.jpg' \/><\/center><br\/>T\u00ecm $m$ \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh $|3-5x| + 6 = 4m + 8$ c\u00f3 nghi\u1ec7m duy nh\u1ea5t","select":[" A. $m = 2$"," B. $m = -2$","C. $m = \\dfrac{-1}{2}$","D. $m = \\dfrac{1}{2}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/span><br\/>Cho ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng $|P(x)| = k$ (trong \u0111\u00f3 $P(x)$ l\u00e0 bi\u1ec3u th\u1ee9c c\u1ee7a $x$, $k$ l\u00e0 m\u1ed9t s\u1ed1 cho tr\u01b0\u1edbc)<br\/>+ N\u1ebfu $k < 0$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m<br\/>+ N\u1ebfu $k = 0$ th\u00ec ta c\u00f3 $|P(x)| = 0 \\Leftrightarrow P(x) = 0$ <br\/>+ N\u1ebfu $k > 0 $ th\u00ec ta c\u00f3 $|P(x)| = k \\Leftrightarrow \\left[\\begin{array}{l} P(x) = k \\\\ P(x) = -k\\end{array} \\right.$ <\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$|3-5x| + 6 = 4m + 8 \\Leftrightarrow |3 - 5x| = 4m + 2$<br\/>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi $4m + 2 = 0 \\Leftrightarrow m = \\dfrac{-1}{2}$ <br\/>V\u1eady \u0111i\u1ec1u ki\u1ec7n c\u1ee7a $m$ l\u00e0 $m = \\dfrac{-1}{2}$ <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1245},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"T\u00ecm $m$ \u0111\u1ec3 $x = 3$ l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{x - 12}{3} - m < 2x - \\dfrac{m - x}{2}$","select":[" A. $m > 21$"," B. $m < 21$","C. $m < -21$","D. $m > -21$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Thay $x = 3$ v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u1edbi \u1ea9n $m$<br\/><b>B\u01b0\u1edbc 2:<\/b> Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u1edbi v\u00e0 t\u00ecm $m$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>V\u00ec $x = 3$ l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh n\u00ean ta c\u00f3:<br\/>$\\dfrac{3 - 12}{3} - m < 2.3 - \\dfrac{m - 3}{2}$<br\/>$\\Leftrightarrow -3 - m < 6 - \\dfrac{m - 3}{2}$<br\/>$\\Leftrightarrow -3 - m < \\dfrac{12 - m + 3}{2}$<br\/> $\\Leftrightarrow 2(-3 - m) < 15 - m$<br\/>$\\Leftrightarrow -6 - 2m < 15 - m$<br\/>$\\Leftrightarrow -2m + m < 15 + 6$<br\/>$\\Leftrightarrow -m < 21$<br\/>$\\Leftrightarrow m > -21$<br\/>V\u1eady \u0111i\u1ec1u ki\u1ec7n c\u1ea7n t\u00ecm c\u1ee7a $m$ l\u00e0 $m > -21$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $m > -21$<\/span> <\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1246},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/5.jpg' \/><\/center><br\/>So s\u00e1nh $a$ v\u00e0 $b$ n\u1ebfu: $-18a + 11 \\geq -18b + 11$","select":[" A. $a \\leq b $"," B. $a \\geq b$","C. $a > b$","D. $a < b$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc c\u1ed9ng v\u00e0 nh\u00e2n c\u1ea3 hai v\u1ebf b\u1ea5t \u0111\u1eb3ng th\u1ee9c cho c\u00f9ng m\u1ed9t s\u1ed1.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>+ Khi c\u1ed9ng c\u00f9ng m\u1ed9t s\u1ed1 v\u00e0o c\u1ea3 hai v\u1ebf c\u1ee7a m\u1ed9t b\u1ea5t \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<br\/>+ Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a m\u1ed9t b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 \u00e2m ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi ng\u01b0\u1ee3c chi\u1ec1u v\u1edbi b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $-18a + 11 \\geq -18b + 11$<br\/>$\\Rightarrow -18a + 11 + (-11) \\geq -18b + 11 + (-11)$<br\/>$\\Rightarrow -18a \\geq -18b \\Rightarrow -18a.\\dfrac{1}{-18} \\leq -18b.\\dfrac{1}{-18} \\Rightarrow a \\leq b$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $a \\leq b$<\/span> ","column":2}]}],"id_ques":1247},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c<br\/>$A = x^2 - 3x$","select":[" A. min$A = \\dfrac{9}{4}$"," B. min$A = \\dfrac{-9}{4}$","C. min$A = \\dfrac{1}{4}$","D. min$A = \\dfrac{-1}{4}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c $A$ v\u1ec1 d\u1ea1ng $[f(x)]^2 + a$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c $A$<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align*}A& = x^2 -3x \\\\&= x^2 -2x\\dfrac{3}{2} + \\left(\\dfrac{3}{2}\\right)^2 - \\left(\\dfrac{3}{2}\\right)^2 \\\\&= \\left(x - \\dfrac{3}{2}\\right)^2 - \\dfrac{9}{4}\\end{align*}$<br\/>L\u1ea1i c\u00f3: $\\left(x - \\dfrac{3}{2}\\right)^2 \\geq 0 \\ \\forall x \\Rightarrow \\left(x - \\dfrac{3}{2}\\right)^2 - \\dfrac{9}{4} \\geq \\dfrac{-9}{4} \\forall x$<br\/>V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $\\dfrac{-9}{4}$<br\/>D\u1ea5u \"=\" x\u1ea3y ra khi $x - \\dfrac{3}{2} = 0 \\Leftrightarrow x = \\dfrac{3}{2}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. min$A = \\dfrac{-9}{4}$<\/span>","column":2}]}],"id_ques":1248},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $A = x^6 - y^6$, bi\u1ebft $x^2 - y^2 = 1$.","select":[" A. min$A = 0$"," B. min$A = 1$","C. min$A = -1$","D. min$A = -3$"],"hint":"S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c t\u1ed5ng c\u1ee7a hai l\u1eadp ph\u01b0\u01a1ng \u0111\u1ec3 khai tri\u1ec3n $A$.","explain":"<span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$\\begin{align*}A& = x^6 - y^6 \\\\&= (x^2)^3 - (y^2)^3 \\\\&= (x^2 - y^2)(x^4 +x^2y^2 + y^4) \\\\&= x^4 + x^2y^2 + y^4 \\\\&= (x^4 - 2x^2y^2 + y^4) + 3x^2y^2 \\\\&= (x^2 - y^2)^2 + 3 x^2y^2 \\\\&= 1 + 3 x^2y^2\\end{align*}$<br\/>L\u1ea1i c\u00f3: $3x^2y^2 \\geq 0 \\ \\forall x \\Rightarrow 1 + 3x^2y^2 \\geq 1 \\forall x$<br\/>V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $1$<br\/>D\u1ea5u \"=\" x\u1ea3y ra khi $x = 0$ ho\u1eb7c $y = 0$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. min$A = 1$<\/span>","column":2}]}],"id_ques":1249},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv3/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $5x + 16 < -6x + 38$","select":[" A. $\\left\\{x \\mid x > 2\\right\\}$"," B. $\\left\\{x \\mid x < 2\\right\\}$","C. $\\left\\{x \\mid x > 22 \\right\\}$","D. $\\left\\{x \\mid x < 22 \\right\\}$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf v\u00e0 quy t\u1eafc nh\u00e2n ho\u1eb7c quy t\u1eafc chia v\u1edbi m\u1ed9t s\u1ed1 \u0111\u1ec3 gi\u1ea3i.","explain":"<span class='basic_left'>Ta c\u00f3 $5x + 16 < -6x + 38$<br\/>$\\Leftrightarrow 5x + 6x < 38 - 16$<br\/>$\\Leftrightarrow 11x < 22$<br\/>$\\Leftrightarrow x < 22 : 11$ <br\/>$\\Leftrightarrow x < 2$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $\\left\\{x \\mid x < 2\\right\\}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. $\\left\\{x \\mid x < 2\\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1250}],"lesson":{"save":0,"level":3}}