{"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}}