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{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Gi\u1ea3 s\u1eed $a < b$, h\u00e3y so s\u00e1nh: $a + 5$ v\u00e0 $b + 5$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $a + 5$ _input_ $b + 5$<\/span>","hint":"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","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$a < b$ $\\Rightarrow a + 5 < b + 5$<br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"<\"<\/span><\/span>"}]}],"id_ques":1071},{"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\u1ea3 s\u1eed $a \\leq b$, h\u00e3y so s\u00e1nh: $a - 8$ v\u00e0 $b - 8$","select":[" A. $a - 8 \\leq b - 8$"," B. $a - 8 \\geq b - 8$","C. $a - 8 = b - 8$"],"hint":" 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","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$ a \\leq b \\Rightarrow a + (-8) \\leq b + (-8) $ hay $a - 8 \\leq b - 8$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $a - 8 \\leq b - 8$<\/span><\/span>","column":3}]}],"id_ques":1072},{"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/bai25/lv2/img\/5.jpg' \/><\/center><br\/>So s\u00e1nh $a$ v\u00e0 $b$ n\u1ebfu: $2a + 12 \\geq 2b + 12$","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 d\u01b0\u01a1ng 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<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $2a + 12 \\geq 2b + 12$<br\/>$\\Rightarrow 2a + 12 + (-12) \\geq 2b + 12 + (-12)$<br\/>$\\Rightarrow 2a \\geq 2b \\Rightarrow 2a.\\dfrac{1}{2} \\geq 2b.\\dfrac{1}{2} \\Rightarrow a \\geq b$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. $a \\geq b$<\/span> ","column":2}]}],"id_ques":1073},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai25/lv2/img\/3.jpg' \/><\/center><br\/>So s\u00e1nh $a$ v\u00e0 $b$ n\u1ebfu: $-5a + 1 > -5b + 1$","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: $-5a + 1 > -5b + 1$<br\/>$\\Rightarrow -5a + 1 + (-1) > -5b + 1 + (-1)$<br\/>$\\Rightarrow -5a > -5b \\Rightarrow -5a.\\dfrac{1}{-5} < -5b.\\dfrac{1}{-5} \\Rightarrow a < b$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $a < b$<\/span> ","column":2}]}],"id_ques":1074},{"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":"S\u1ed1 $a$ l\u00e0 s\u1ed1 \u00e2m hay s\u1ed1 d\u01b0\u01a1ng n\u1ebfu: $14a + 1 < 18a + 1$","select":[" A. S\u1ed1 d\u01b0\u01a1ng"," B. S\u1ed1 \u00e2m"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>+ Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<br\/>+ Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a 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\u1eaft \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $14a + 1 < 18a + 1$<br\/>$\\Rightarrow 14a + 1 + (-1) < 18a + 1 + (-1) \\\\ \\Rightarrow 14a < 18a$<br\/>M\u00e0 $14 < 18$<br\/>$ \\Rightarrow a > 0$ hay $a$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. S\u1ed1 d\u01b0\u01a1ng<\/span>","column":2}]}],"id_ques":1075},{"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":"S\u1ed1 $a$ l\u00e0 s\u1ed1 \u00e2m hay s\u1ed1 d\u01b0\u01a1ng n\u1ebfu: $-2a - 3 < -4a - 3$","select":[" A. S\u1ed1 d\u01b0\u01a1ng"," B. S\u1ed1 \u00e2m"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>+ Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<br\/>+ Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a 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\u1eaft \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 cho<\/span> <br\/><br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $-2a - 3 < -4a - 3$<br\/>$\\Rightarrow -2a - 3 + 3 < -4a - 3 + 3 \\\\ \\Rightarrow -2a < -4a$<br\/>M\u00e0 $-2 > -4$<br\/>$ \\Rightarrow a < 0$ hay $a$ l\u00e0 s\u1ed1 \u00e2m<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. S\u1ed1 \u00e2m<\/span>","column":2}]}],"id_ques":1076},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho $m < n$, h\u00e3y so s\u00e1nh: $3m + 2$ v\u00e0 $3n + 2$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $3m + 2$ _input_ $3n + 2$","hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$m < n$ $\\Rightarrow 3m < 3n \\Rightarrow 3m + 2 < 3n + 2$<br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"<\"<\/span><\/span>"}]}],"id_ques":1077},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Cho $m < n$, h\u00e3y so s\u00e1nh: $-2m - 8$ v\u00e0 $-2n - 9$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $-2m - 8$ _input_ $-2n - 9$","hint":"","explain":"<span class='basic_left'>Ta c\u00f3: $m < n$ v\u00e0 $-2 < 0$ $\\Rightarrow -2m > -2n \\Rightarrow -2m + (-8) > -2n + (-8)$ hay $-2m - 8 > -2n - 8$ <b>(1)<\/b><br\/>L\u1ea1i c\u00f3: $-8 > -9 \\Rightarrow -8 + (-2n) > (-9) + (-2n)$ hay $-2n - 8 > -2n - 9$ <b>(2)<\/b><br\/>T\u1eeb (1) v\u00e0 (2) $ \\Rightarrow -2m - 8 > -2n - 9$<br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\">\"<\/span><\/span>"}]}],"id_ques":1078},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c<br\/>$A = x^2 + 4x + 15$","select":[" A. min$A = 10$"," B. min$A = 15$","C. min$A = 11$","D. min$A = 2$"],"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\/>$\\begin{align*}A& = x^2 + 4x + 15 \\\\&= x^2 + 4x + 4 + 11 \\\\&= (x + 2)^2 + 11\\end{align*}$<br\/>L\u1ea1i c\u00f3: $(x + 2)^2 \\geq 0 \\ \\forall x \\Rightarrow (x + 2)^2 + 11 \\geq 11 \\forall x$<br\/>V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 11<br\/>D\u1ea5u \"=\" x\u1ea3y ra khi $x + 2 = 0 \\Leftrightarrow x = -2$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. min$A = 11$<\/span>","column":2}]}],"id_ques":1079},{"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":"T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c<br\/>$A = x^2 - 5x + 12$","select":[" A. min$A = \\dfrac{25}{4}$"," B. min$A = \\dfrac{23}{4}$","C. min$A = 12$","D. min$A = 18$"],"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\/>$\\begin{align*}A& = x^2 -5x + 12 \\\\&= x^2 -2x\\dfrac{5}{2} + \\left(\\dfrac{5}{2}\\right)^2 - \\left(\\dfrac{5}{2}\\right)^2 + 12 \\\\&= \\left(x - \\dfrac{5}{2}\\right)^2 + \\dfrac{23}{4}\\end{align*}$<br\/>L\u1ea1i c\u00f3: $\\left(x - \\dfrac{5}{2}\\right)^2 \\geq 0 \\ \\forall x \\Rightarrow \\left(x - \\dfrac{5}{2}\\right)^2 + \\dfrac{23}{4} \\geq \\dfrac{23}{4} \\forall x$<br\/>V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$ l\u00e0 $\\dfrac{23}{4}$<br\/>D\u1ea5u \"=\" x\u1ea3y ra khi $x - \\dfrac{5}{2} = 0 \\Leftrightarrow x = \\dfrac{5}{2}$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. min$A = \\dfrac{23}{4}$<\/span>","column":2}]}],"id_ques":1080},{"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":"Cho $a > 0$, h\u00e3y so s\u00e1nh: $a + \\dfrac{1}{a}$ v\u00e0 $2$","select":[" A. $a + \\dfrac{1}{a} \\geq 2$"," B. $a + \\dfrac{1}{a} > 2$","C. $a + \\dfrac{1}{a} < 2$","D. $a + \\dfrac{1}{a} \\leq 2$"],"hint":"","explain":"<span class='basic_left'>L\u1eadp hi\u1ec7u: $a + \\dfrac{1}{a} - 2$. Ta c\u00f3:<br\/>$a + \\dfrac{1}{a} - 2 = \\dfrac{a^2 + 1 - 2a}{a} = \\dfrac{(a - 1)^2}{a}$<br\/>V\u00ec $(a - 1)^2 \\geq 0 \\ \\forall x$ v\u00e0 $a > 0$ n\u00ean $\\dfrac{(a - 1)^2}{a} \\geq 0$<br\/>Do \u0111\u00f3: $a + \\dfrac{1}{a} - 2 \\geq 0 \\Rightarrow a + \\dfrac{1}{a} \\geq 2$ <br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> A. $a + \\dfrac{1}{a} \\geq 2$<\/span><\/span>","column":2}]}],"id_ques":1081},{"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":"Cho $0 < a < b$, h\u00e3y so s\u00e1nh: $a^2$ v\u00e0 $a.b$","select":[" A. $a^2 \\geq ab$"," B. $a^2 = ab$","C. $a^2 > ab$","D. $a^2 < ab$"],"hint":"D\u1ef1a v\u00e0o b\u1ea5t \u0111\u1eb3ng th\u1ee9c $a < b$ v\u00e0 $a > 0$ \u0111\u1ec3 so s\u00e1nh $a^2$ v\u00e0 $a.b$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $a < b$ v\u00e0 $a > 0$ $ \\Rightarrow a.a < b.a \\Rightarrow a^2 < ab$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $a^2 < ab$<\/span><\/span> <br\/><\/span>","column":2}]}],"id_ques":1082},{"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":"Cho $0 < a < b$, h\u00e3y so s\u00e1nh: $a^2$ v\u00e0 $b^2$","select":[" A. $a^2 \\geq b^2$"," B. $a^2 = b^2$","C. $a^2 > b^2$","D. $a^2 < b^2$"],"hint":"S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t b\u1eafc c\u1ea7u: c\u00f9ng so s\u00e1nh v\u1edbi $ab$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $a < b$ v\u00e0 $a > 0$ $ \\Rightarrow a.a < b.a \\Rightarrow a^2 < ab$ <b>(1)<\/b><br\/>L\u1ea1i c\u00f3: $a < b$ v\u00e0 $b > 0$ $\\Rightarrow a.b < b.b \\Rightarrow ab < b^2$ <b>(2)<\/b><br\/>T\u1eeb (1) v\u00e0 (2) $\\Rightarrow a^2 < b^2$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'> D. $a^2 < b^2$<\/span><\/span> <br\/><\/span>","column":2}]}],"id_ques":1083},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"So s\u00e1nh $m^2$ v\u00e0 $m$ n\u1ebfu: $m$ l\u1edbn h\u01a1n $1$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $m^2$ _input_ $m$","hint":"S\u1eed d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c $m > 1$ \u0111\u1ec3 so s\u00e1nh $m^2$ v\u00e0 $m$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $m > 1$ v\u00e0 $m > 0$ $\\Rightarrow m.m > 1.m \\Rightarrow m^2 > m$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\">\"<\/span><\/span> <br\/><\/span>"}]}],"id_ques":1084},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"So s\u00e1nh $m^2$ v\u00e0 $m$ n\u1ebfu: $m$ d\u01b0\u01a1ng nh\u01b0ng nh\u1ecf h\u01a1n $1$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $m^2$ _input_ $m$","hint":"S\u1eed d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c $m < 1$ v\u00e0 $m > 0$ \u0111\u1ec3 so s\u00e1nh $m^2$ v\u00e0 $m$.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Khi nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $m < 1$ v\u00e0 $m > 0$ $\\Rightarrow m.m < 1.m \\Rightarrow m^2 < m$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"<\"<\/span><\/span> <br\/><\/span>"}]}],"id_ques":1085},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (<, >) v\u00e0o \u00f4 tr\u1ed1ng sao cho \u0111\u00fang","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai25/lv2/img\/3.jpg' \/><\/center><br\/> $(0,5)^2$ _input_ $0,5$","hint":"S\u1eed d\u1ee5ng quy t\u1eafc 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 nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $0,5 < 1$ v\u00e0 $0,5 > 0$ $\\Rightarrow 0,5.0,5 < 1.0,5 \\Rightarrow (0,5)^2 < 0,5$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\"<\"<\/span><\/span> <br\/><\/span>"}]}],"id_ques":1086},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (<, >) v\u00e0o \u00f4 tr\u1ed1ng sao cho \u0111\u00fang","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai25/lv2/img\/5.jpg' \/><\/center><br\/> $(1,6)^2$ _input_ $1,6$","hint":"S\u1eed d\u1ee5ng quy t\u1eafc 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 nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $1,6 > 1$ v\u00e0 $1,6 > 0$ $\\Rightarrow 1,6.1,6 > 1.1,6 \\Rightarrow (1,6)^2 > 1,6$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\">\"<\/span><\/span> <br\/><\/span>"}]}],"id_ques":1087},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t","t"]],"list":[{"point":5,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":[" $a < b$ th\u00ec $a - 7 < b - 7 $ "," $a < b$ th\u00ec $-9a < -9b $ "," $ a > b$ th\u00ec $3a > 3b$ ","$ a > b$ th\u00ec $a + 15 > b + 15$"],"hint":"","explain":["$a < b$ th\u00ec $a - 7 < b - 7$ (\u0110\u00fang). V\u00ec $a < b \\Rightarrow a + (-7) < b + (-7) \\Rightarrow a - 7 < b - 7 $","<br\/> $a < b$ th\u00ec $-9a < -9b$ (Sai). V\u00ec $a < b$ v\u00e0 $-9 < 0$ $\\Rightarrow a.(-9) > b.(-9) \\Rightarrow -9a > -9b$ ","<br\/> $ a > b$ th\u00ec $3a > 3b$ (\u0110\u00fang). V\u00ec $a > b$ v\u00e0 $3 > 0$ $\\Rightarrow a.3 > b.3 \\Rightarrow 3a > 3b$ ","<br\/> $ a > b$ th\u00ec $a + 15 > b + 15$ (\u0110\u00fang) "]}]}],"id_ques":1088},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["f","f","t","t"]],"list":[{"point":5,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":[" $a < b$ th\u00ec $a - 9 > b - 9 $ "," $a < b$ th\u00ec $-5a < -5b $ "," $ a > b$ th\u00ec $-9a < -9b$ ","$ a > b$ th\u00ec $27a + 1 > 27b + 1$"],"hint":"","explain":["$a < b$ th\u00ec $a - 9 > b - 9 $ (Sai). V\u00ec $a < b \\Rightarrow a + (-9) < b + (-9) \\Rightarrow a - 9 < b - 9 $","<br\/> $a < b$ th\u00ec $-5a < -5b$ (Sai). V\u00ec $a < b$ v\u00e0 $-5 < 0$ $\\Rightarrow a.(-5) > b.(-5) \\Rightarrow -5a > -5b$ ","<br\/> $ a > b$ th\u00ec $-9a < -9b$ (\u0110\u00fang). V\u00ec $a > b$ v\u00e0 $-9 < 0$ $\\Rightarrow a.(-9) < b.(-9) \\Rightarrow -9a < -9b$ ","<br\/> $ a > b$ th\u00ec $27a + 1 > 27b + 1$ (\u0110\u00fang). V\u00ec $ a > b$ v\u00e0 $27 > 0$ $\\Rightarrow 27a > 27b \\Rightarrow 27a + 1 > 27b + 1$ "]}]}],"id_ques":1089},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (<, >) v\u00e0o \u00f4 tr\u1ed1ng sao cho \u0111\u00fang","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai25/lv2/img\/5.jpg' \/><\/center><br\/> Bi\u1ebft $2a > 10$. So s\u00e1nh $a$ v\u00e0 $5$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $a$ _input_ $5$","hint":"S\u1eed d\u1ee5ng quy t\u1eafc 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 nh\u00e2n c\u1ea3 hai v\u1ebf c\u1ee7a b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c b\u1ea5t \u0111\u1eb3ng th\u1ee9c m\u1edbi c\u00f9ng chi\u1ec1u v\u1edbi b\u1eaft \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: $2a > 10$ v\u00e0 $\\dfrac{1}{2} > 0$ $\\Rightarrow 2a\\dfrac{1}{2} > 10\\dfrac{1}{2} \\Rightarrow a > 5$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>\">\"<\/span><\/span> <br\/><\/span>"}]}],"id_ques":1090}],"lesson":{"save":0,"level":2}}

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Câu hỏi này theo dạng chọn đáp án đúng, sau khi đọc xong câu hỏi, bạn bấm vào một trong số các đáp án mà chương trình đưa ra bên dưới, sau đó bấm vào nút gửi để kiểm tra đáp án và sẵn sàng chuyển sang câu hỏi kế tiếp

Trả lời đúng trong khoảng thời gian quy định bạn sẽ được + số điểm như sau:
Trong khoảng 1 phút đầu tiên + 5 điểm
Trong khoảng 1 phút -> 2 phút + 4 điểm
Trong khoảng 2 phút -> 3 phút + 3 điểm
Trong khoảng 3 phút -> 4 phút + 2 điểm
Trong khoảng 4 phút -> 5 phút + 1 điểm

Quá 5 phút: không được cộng điểm

Tổng thời gian làm mỗi câu (không giới hạn)

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Bấm vào đây nếu phát hiện có lỗi hoặc muốn gửi góp ý