{"segment":[{"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/lop7/toan/daiso/bai12/lv3/img\/4.jpg' \/><\/center> Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang: ","select":["A. $ \\mathbb{Z} \\subset \\mathbb{N} \\subset \\mathbb{Q} $ ","B. $ \\mathbb{I} \\subset \\mathbb{Q} \\subset \\mathbb{R}$ ","C. $ \\mathbb{Z} \\subset \\mathbb{Q} \\subset \\mathbb{R}$ ","D. $ \\mathbb{I} \\subset \\mathbb{Q}$ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/>* $\\mathbb{N}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean, bao g\u1ed3m $ 0 ; 1 ; 2 ; 3 ; \u2026 $ <br\/> *$\\mathbb{Z}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 nguy\u00ean, bao g\u1ed3m $\u2026,-2 ;-1 ;0 ;1 ;2 ;\u2026$ <br\/> * $\\mathbb{Q}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9, l\u00e0 s\u1ed1 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ v\u1edbi $a,b \u2208 \\mathbb{Z} , b \u2260 0$. <br\/> * $\\mathbb{I}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 v\u00f4 t\u1ec9 l\u00e0 s\u1ed1 vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n kh\u00f4ng tu\u1ea7n ho\u00e0n. <br\/> *$\\mathbb{R}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 th\u1ef1c bao g\u1ed3m c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 c\u00e1c s\u1ed1 v\u00f4 t\u1ec9. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3 quan h\u1ec7 gi\u1eefa c\u00e1c t\u1eadp h\u1ee3p l\u00e0: <br\/> $\\mathbb{N} \\subset \\mathbb{Z} \\subset \\mathbb{Q} \\subset \\mathbb{R} $ v\u00e0 $\\mathbb{I} \\subset \\mathbb{R}$ <br\/> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <br\/> $ \\mathbb{Z} \\subset \\mathbb{Q} \\subset \\mathbb{R}$ <br\/> <\/span><\/span> ","column":2}],"id_ques":551},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" Gi\u00e1 tr\u1ecb c\u1ee7a $(-0,5)^{3}.(-0,5)$ b\u1eb1ng: ","select":["A. $ (-0,5)^{2}$ ","B. $ (0,5)^{4}$ ","C. $ -(0,5)^{4}$","D. $ (0,5)^{3}$ "],"hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c: $x^{m}.x^{n} = x^{m+n} $ ","explain":" Ta c\u00f3: $(-0,5)^{3}.(-0,5) = (-0,5)^{3 + 1} $$= (-0,5)^{4} = (0,5)^{4}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> <span class='basic_left'> <i> L\u01b0u \u00fd: <\/i> $\\bullet$ L\u0169y th\u1eeba b\u1eadc ch\u1eb5n c\u1ee7a m\u1ed9t s\u1ed1 \u00e2m l\u00e0 m\u1ed9t s\u1ed1 d\u01b0\u01a1ng. <br\/> $\\qquad \\quad \\bullet$ L\u0169y th\u1eeba b\u1eadc l\u1ebb c\u1ee7a m\u1ed9t s\u1ed1 \u00e2m l\u00e0 m\u1ed9t s\u1ed1 \u00e2m. <\/span> ","column":2}],"id_ques":552},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["sqrt","x_sqrt","frac","sqr","x_"],"ques":" Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh: <br\/> $A = 16\\dfrac{2}{7} : \\left( -\\dfrac{3}{5}\\right) - 28\\dfrac{2}{7} : \\left( -\\dfrac{3}{5}\\right) $ <br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $A$ = _input_ ","hint":"Nh\u00f3m m\u1ed9t c\u00e1ch h\u1ee3p l\u00ed.","explain":"Ta c\u00f3: $A = 16\\dfrac{2}{7} : \\left( -\\dfrac{3}{5}\\right) - 28\\dfrac{2}{7} : \\left( -\\dfrac{3}{5}\\right) \\\\ = \\left( 16\\dfrac{2}{7} - 28\\dfrac{2}{7} \\right) : \\left( -\\dfrac{3}{5}\\right) \\\\ = \\left( 16 + \\dfrac{2}{7} - 28 - \\dfrac{2}{7} \\right) . \\left( \\dfrac{-5}{3}\\right) \\\\ = -12 . \\dfrac{-5}{3} \\\\ = 20$ <br\/> <br\/> <span class='basic_pink'> K\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh l\u00e0: 20 <\/span><\/span> "}],"id_ques":553},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-2"],["3"]]],"list":[{"point":10,"width":50,"ques":" T\u00ecm $x$, bi\u1ebft $ \\dfrac{3}{4} + \\dfrac{2}{5}x = \\dfrac{29}{60} $ <br\/> V\u1eady $x$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u00e0i to\u00e1n t\u00ecm x <\/b> <br\/> B\u01b0\u1edbc 1. Chuy\u1ec3n c\u00e1c h\u1ea1ng t\u1eed ch\u1ee9a $x$ sang m\u1ed9t v\u1ebf, c\u00e1c h\u1eb1ng s\u1ed1 sang v\u1ebf kia. <br\/> B\u01b0\u1edbc 2. Thu g\u1ecdn v\u00e0 t\u00ecm $x$. <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <br\/> Ta c\u00f3: $ \\dfrac{3}{4} + \\dfrac{2}{5}x = \\dfrac{29}{60} \\\\ \\Rightarrow \\dfrac{2}{5}x = \\dfrac{29}{60} - \\dfrac{3}{4} \\\\ \\Rightarrow \\dfrac{2}{5}x = \\dfrac{-4}{15} \\\\ \\Rightarrow x = \\dfrac{-4}{15} : \\dfrac{2}{5} \\\\ \\Rightarrow x = \\dfrac{-2}{3}$<\/span>"}],"id_ques":554},{"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 $x$ bi\u1ebft: <br\/> $1,573 - |x - 0,573| = 0 $ ","select":["A. $x = -2,146$ ho\u1eb7c $x = -1 $ ","B. $x = 2,146$ ho\u1eb7c $x = 1 $ ","C. $x = -2,146$ ho\u1eb7c $x = 1 $ ","D. $x = 2,146$ ho\u1eb7c $x = -1 $ "],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> N\u1ebfu $|x| = a$(v\u1edbi $a \\neq 0$) <br\/> th\u00ec $x = \\pm a$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $1,573 - |x - 0,573| = 0 \\\\ \\Rightarrow |x - 0,573| = 1,573 $ <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $ x - 0,573 = 1,573 \\Rightarrow x = 1,573 + 0,573 = 2,146 $ <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $ x - 0,573 = -1,573 \\Rightarrow x = -1,573 + 0,573 = -1 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 $x = 2,146$ ho\u1eb7c $x = -1 $ <br\/><br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D <\/span> <span class='basic_pink'> <\/span> ","column":2}],"id_ques":555},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" So s\u00e1nh hai l\u0169y th\u1eeba <br\/> $2^{600}$ v\u00e0 $3^{400}$ ta \u0111\u01b0\u1ee3c: ","select":[" $2^{600}$ > $3^{400}$ "," $2^{600}$ < $3^{400}$ "," $2^{600}$ = $3^{400}$ "],"hint":"\u0110\u01b0a v\u1ec1 so s\u00e1nh hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> Quy t\u1eafc ph\u00e9p to\u00e1n v\u1ec1 l\u0169y th\u1eeba. <\/b> <br\/> L\u0169y th\u1eeba c\u1ee7a l\u0169y th\u1eeba: <br\/> $ x^{m.n} = (x^{m})^{n} (x \\in \\mathbb{Q}; m,n \\in \\mathbb{N}) $ <\/span><br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $2^{600} = 2^{3.200} = (2^{3})^{200} = 8^{200} \\\\ 3^{400} = 3^{2.200} = (3^{2})^{200} = 9^{200} $ <br\/> V\u00ec $ 8^{200} < 9^{200}$ <br\/> n\u00ean $ 2^{600} < 3^{400}$ <br\/><br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span> ","column":3}],"id_ques":556},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":" Khi n\u00f3i c\u00e1c s\u1ed1 a; b; c t\u1ec9 l\u1ec7 v\u1edbi c\u00e1c s\u1ed1 2; 3; 5 ngh\u0129a l\u00e0: ","select":["A. a : b : c = 2 : 3 : 5 ","B. a : 2 = b : 3 = c : 5 ","C. $ \\dfrac{a}{2} = \\dfrac{b}{3} = \\dfrac{c}{5} $ ","D. T\u1ea5t c\u1ea3 \u0111\u1ec1u \u0111\u00fang. "],"hint":"Xem b\u00e0i t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau.","explain":" C\u00e1c s\u1ed1 $a; b; c$ t\u1ec9 l\u1ec7 v\u1edbi c\u00e1c s\u1ed1 $2; 3; 5,$ th\u00ec ta vi\u1ebft \u0111\u01b0\u1ee3c: <br\/> $a : b : c = 2 : 3 : 5$ <br\/> $a : 2 = b : 3 = c : 5$ <br\/> $ \\dfrac{a}{2} = \\dfrac{b}{3} = \\dfrac{c}{5} $ <br\/><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span> ","column":2}],"id_ques":557},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["8"],["15"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm a, b, c bi\u1ebft: <br\/> $3a - 5b + 7c = 86 $ v\u00e0 $\\dfrac{a+3}{5} = \\dfrac{b-2}{3} = \\dfrac{c-1}{7} $ <br\/> <br\/> $ a = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ b = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ c = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} $ ","hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" <span class='basic_left'> Ta c\u00f3: $\\dfrac{a+3}{5} = \\dfrac{b-2}{3} = \\dfrac{c-1}{7} $ <br\/> Suy ra $\\dfrac{3(a+3)}{3.5} = \\dfrac{5(b-2)}{5.3} = \\dfrac{7(c-1)}{7.7} \\\\ \\Rightarrow \\dfrac{3a+9}{15} = \\dfrac{5b-10}{15} = \\dfrac{7c-7}{49}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{3a+9}{15} = \\dfrac{5b-10}{15} = \\dfrac{7c-7}{49}$ = $ \\dfrac{3a+9-5b+10+7c-7}{15-15+49} $ <br\/> $ = \\dfrac{(3a-5b+7c)+ 12}{15-15+49} $ <br\/> $ = \\dfrac{86+12}{49} = 2 $ <br\/> Do \u0111\u00f3: <br\/> $\\dfrac{a+3}{5} = 2 \\Rightarrow a + 3 = 10 \\Rightarrow a = 7 $ <br\/> $ \\dfrac{b-2}{3} = 2 \\Rightarrow b - 2 = 6 \\Rightarrow b = 8 $ <br\/> $ \\dfrac{c-1}{7} = 2 \\Rightarrow c - 1 = 14 \\Rightarrow c = 15 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a, b, c$ l\u00e0: $\\begin{cases} a = 7 \\\\ b = 8 \\\\ c = 15 \\end{cases}$ <\/span><\/span> "}],"id_ques":558},{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2017"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Cho $M = 2017 + \\sqrt{2016-x} .$ T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $M$? <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> min $M$ = $ \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} $ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t: $\\sqrt{A} \\geq 0 $ <br\/> (D\u1ea5u ''='' x\u1ea3y ra khi v\u00e0 ch\u1ec9 khi A = 0). <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> M c\u00f3 ngh\u0129a khi $ 2016 - x \\geq 0 \\Rightarrow x \\leq 2016 $ <br\/> V\u1edbi $x \\leq 2016 $ th\u00ec $\\sqrt{2016-x} \\geq 0 $ <br\/> Suy ra $ 2017 + \\sqrt{2016-x} \\geq 2017 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a M b\u1eb1ng 2017 khi $ 2016 - x = 0 $ hay $x = 2016 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady min $M = 2017 $ khi $x = 2016 $ <\/span><\/span>"}],"id_ques":559},{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" \u01af\u1edbc l\u01b0\u1ee3ng gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $ M = \\dfrac{\\sqrt{86}}{2,8 . 16,18} ?$ <br\/> (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t) ","select":["A. 0,2 ","B. 1,2 ","C. 0,1 ","D. 1 "],"explain":"Ta c\u00f3: $ M = \\dfrac{\\sqrt{86}}{2,8 . 16,18} \\approx \\dfrac{9}{3.16} = \\dfrac{3}{16} \\approx \\dfrac{1}{5} = 0,2 $ <br\/> V\u1eady $ M \\approx 0,2$ (l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 nh\u1ea5t). <br\/><br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span> ","column":2}],"id_ques":560}],"id_ques":0}],"lesson":{"save":1,"level":3,"time":44}}