{"common":{"save":0,"post_id":"964","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"191","post_id":"964","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":[[2]],"list":[{"point":10,"ques":" <center><img src='img\/2.jpg' \/><\/center> V\u1edbi $x > 0, y < 0$ v\u00e0 $|x| = |y|$ th\u00ec: ","select":["A. $ x^{2}y > 0$","B. $ x + y = 0 $","C. $ x - y = 0 $","D. $ x = \\pm y $ "],"hint":" $|x| = |y| \\Leftrightarrow x = \\pm y $ ","explain":" Ta c\u00f3 : $|x| = |y|$ <br\/> Suy ra $x = y $ ho\u1eb7c $x = -y $ (1) <br\/> M\u00e0 theo gi\u1ea3 thi\u1ebft c\u00f3 $x > 0, y < 0$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) suy ra $x = -y $ <br\/> Hay $x + y = 0 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span> <br\/>","column":2}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:44"},{"id":"192","post_id":"964","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","options":{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"],["3"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":" T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $ C = \\dfrac{1}{3-|x-2|} \\text { (bi\u1ebft C > 0) } $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> min C = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u00c1p d\u1ee5ng: $|x| < a \\Rightarrow -a < x < a $","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> T\u00ccM GI\u00c1 TR\u1eca NH\u1ece NH\u1ea4T C\u1ee6A BI\u1ec2U TH\u1ee8C CH\u1ee8A D\u1ea4U GI\u00c1 TR\u1eca TUY\u1ec6T \u0110\u1ed0I <\/b> <br\/> $\\quad T = a + |f(x)| $ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c c\u00f3 ch\u1ee9a bi\u1ebfn $x$ <br\/> V\u00ec $|f(x)| \\geq 0 \\,\\,\\forall x \\in \\mathbb{Q}$ n\u00ean $T \\geq a$ <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $T$ b\u1eb1ng $a$ khi $f(x) = 0$ (ta ph\u1ea3i t\u00ecm $x$ \u0111\u1ec3 $f(x) = 0 $). <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <br\/> $ C = \\dfrac{1}{3-|x-2|}$ (bi\u1ebft C > 0) <br\/> C\u00f3 $C > 0 \\Rightarrow 3 - |x - 2| > 0 $ <br\/> $\\Rightarrow |x - 2| < 3 $ <br\/> $ \\Rightarrow -3 < x - 2 < 3 $ <br\/> $\\Rightarrow -1 < x < 5$ (*) <br\/> V\u00ec C > 0 n\u00ean C nh\u1ecf nh\u1ea5t khi $3 - |x -2|$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng l\u1edbn nh\u1ea5t. <br\/> V\u00ec $|x - 2| \\geq 0 \\quad \\forall x \\in \\mathbb{Q}$ n\u00ean $ -|x - 2| \\leq 0 $ <br\/> $ \\Rightarrow 0 < 3 - |x - 2| \\leq 3 \\forall x \\in \\mathbb{Q} $ <br\/> $\\Rightarrow \\dfrac{1}{3-|x-2|} \\geq \\dfrac{1}{3},$ $\\forall x \\in \\mathbb{Q}$ <br\/> Hay $C \\geq \\dfrac{1}{3,}$ $\\forall x \\in \\mathbb{Q}$ <br\/> V\u1eady GTNN c\u1ee7a $C = \\dfrac{1}{3}$ khi $x - 2 = 0$ hay $x = 2$ (th\u1ecfa m\u00e3n (*)) <br\/> <br\/> <span class='basic_pink'> V\u1eady GTNN c\u1ee7a C l\u00e0 $\\dfrac{1}{3}$ khi $x = 2 $<\/span><\/span> <br\/>"}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:44"},{"id":"193","post_id":"964","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","options":{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":" T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c: $ B = |x + 1| + 2|6,9 - 3y| + 3 $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> min B = _input_ ","hint":"\u00c1p d\u1ee5ng: $|f(x)| \\geq 0 \\forall x \\in \\mathbb{Q}$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> T\u00ccM GI\u00c1 TR\u1eca NH\u1ece NH\u1ea4T C\u1ee6A BI\u1ec2U TH\u1ee8C CH\u1ee8A D\u1ea4U GI\u00c1 TR\u1eca TUY\u1ec6T \u0110\u1ed0I <\/b> <br\/> $\\quad T = a + |f(x)| $ v\u1edbi $a$ l\u00e0 h\u1eb1ng s\u1ed1, $f(x)$ l\u00e0 bi\u1ec3u th\u1ee9c c\u00f3 ch\u1ee9a bi\u1ebfn $x$ <br\/> V\u00ec $|f(x)| \\geq 0\\,\\, \\forall x \\in \\mathbb{Q}$ n\u00ean $T \\geq a$ <br\/> Khi \u0111\u00f3 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a $T$ b\u1eb1ng $a$ khi $f(x) = 0$ (ta ph\u1ea3i t\u00ecm $x$ \u0111\u1ec3 $f(x) = 0 $). <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <br\/> $B = |x + 1| + 2|6,9 - 3y| + 3 $ <br\/> Ta c\u00f3: $|x + 1| \\geq 0,$ v\u1edbi $\\forall x \\in \\mathbb{Q}$ <br\/> $|6,9 - 3y| \\geq 0,$ v\u1edbi $\\forall y \\in \\mathbb{Q}$ <br\/> $\\Rightarrow B = |x + 1| + 2|6,9 - 3y| + 3 \\geq 0 + 2.0 + 3 = 3$ <br\/> Do \u0111\u00f3 GTNN c\u1ee7a $B = 3$ <br\/> D\u1ea5u ''='' x\u1ea3y ra $\\Leftrightarrow \\begin{cases} x + 1 = 0 \\Rightarrow x = -1 \\\\ 6,9 - 3y = 0 \\Rightarrow y = 6,9 : 3 = 2,3 \\end{cases} $<br\/> <br\/> <span class='basic_pink'> V\u1eady GTNN c\u1ee7a B l\u00e0 $3$ khi $x = -1; y = 2,3$<\/span><\/span> <br\/>"}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:44"}]}