{"common":{"save":0,"post_id":"1018","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"441","post_id":"1018","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","options":{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["11"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Cho $A = \\sqrt{x+2} + \\dfrac{3}{11}.$ T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $A$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> Min A = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":" \u00c1p d\u1ee5ng: $A \\geq m $ suy ra $min A = m $","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> - T\u00ecm $x$ \u0111\u1ec3 A c\u00f3 ngh\u0129a. <br\/> - \u00c1p d\u1ee5ng: $A \\geq m $ suy ra min A = m <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> A c\u00f3 ngh\u0129a khi $x + 2 \\geq 0 \\Rightarrow x \\geq -2$ <br\/> V\u1edbi $x \\geq -2 $ th\u00ec $\\sqrt{x+2} \\geq 0 $ <br\/> Suy ra $ \\sqrt{x+2} + \\dfrac{3}{11} \\geq \\dfrac{3}{11}$ <br\/> V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $ A = \\dfrac{3}{11}$ khi $x+2 = 0 $ hay $x = - 2$ <br\/> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $\\dfrac{3}{11}$ khi $x = -2 $ <\/span><\/span>"}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:47"},{"id":"442","post_id":"1018","mon_id":"0","chapter_id":"0","question":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","options":{"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":" T\u00ecm s\u1ed1 nguy\u00ean $x$ \u0111\u1ec3 $B = \\dfrac{\\sqrt{x} - 3}{\\sqrt{x} + 2}$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean.","select":["A. $x = 9 $ ","B. $x \\in \\{ -1; 9 \\} $ ","C. $x \\in \\{ -1; 9; 49 \\} $ ","D. $x \\in \\{ 1; 9 \\} $ "],"hint":" \u0110\u1ec3 $\\dfrac{a}{b}$ l\u00e0 s\u1ed1 nguy\u00ean th\u00ec $b$ ph\u1ea3i l\u00e0 \u01b0\u1edbc c\u1ee7a $a$","explain":" <span class='basic_left'><span class='basic_green'> B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $B = \\dfrac{\\sqrt{x} - 3}{\\sqrt{x} + 2} \\\\ = \\dfrac{\\sqrt{x}+2-5}{\\sqrt{x}+2} = 1 - \\dfrac{5}{\\sqrt{x}+2}$ <br\/> \u0110\u1ec3 $ B \\in \\mathbb{Z}$ th\u00ec ($\\sqrt{x} + 2$) ph\u1ea3i thu\u1ed9c $\\mathbb{Z}$ v\u00e0 l\u00e0 \u01af(5) = $\\{ \\pm1; \\pm 5 \\}$ <br\/> V\u00ec $\\sqrt{x} + 2 > 0$ n\u00ean ch\u1ec9 c\u00f3 hai tr\u01b0\u1eddng h\u1ee3p: <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $\\sqrt{x} + 2 = 1 \\Leftrightarrow \\sqrt{x} = -1 \\Rightarrow$ kh\u00f4ng c\u00f3 x th\u1ecfa m\u00e3n. <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $\\sqrt{x} + 2 = 5 \\Leftrightarrow \\sqrt{x} = 3 \\Rightarrow x = 9$ (th\u1ecfa m\u00e3n). <br\/> V\u1eady \u0111\u1ec3 $B \\in \\mathbb{Z}$ th\u00ec $x = 9 $<br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:47"},{"id":"443","post_id":"1018","mon_id":"0","chapter_id":"0","question":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","options":{"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 $x$, bi\u1ebft $\\sqrt{1,69} . \\left(2\\sqrt{x} + \\sqrt{\\dfrac{81}{121}} \\right) = \\dfrac{13}{10}?$ ","select":["A. $x = \\dfrac{9}{11}$ ","B. $x = \\dfrac{1}{11}$ ","C. $x = \\dfrac{2}{11}$","D. $x = \\dfrac{1}{121}$"],"explain":" <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\sqrt{1,69} . \\left(2\\sqrt{x} + \\sqrt{\\dfrac{81}{121}} \\right) = \\dfrac{13}{10} \\\\ \\Leftrightarrow 1,3 . \\left(2\\sqrt{x} + \\dfrac{9}{11}\\right) = 1,3 \\\\ \\Leftrightarrow 2\\sqrt{x} + \\dfrac{9}{11} = 1 \\\\ \\Leftrightarrow 2\\sqrt{x} = 1 - \\dfrac{9}{11} = \\dfrac{2}{11} \\\\ \\Leftrightarrow \\sqrt{x} = \\dfrac{2}{11} : 2 = \\dfrac{1}{11} \\\\ \\Leftrightarrow x = \\left(\\dfrac{1}{11}\\right)^{2} = \\dfrac{1}{121} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:47"}]}