{"common":{"save":0,"post_id":"1021","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"491","post_id":"1021","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":" So s\u00e1nh hai t\u1ed5ng A v\u00e0 B n\u1ebfu: <br\/> $A = \\sqrt{20+1} + \\sqrt{40+2} + \\sqrt{60+3}$ <br\/> v\u00e0 $B = (\\sqrt{1} + \\sqrt{2} + \\sqrt{3}) + $ $(\\sqrt{20} + \\sqrt{40} + \\sqrt{60}) $ ","select":["A. A < B ","B. A > B","C. A = B "],"hint":"Ta c\u00f3: $\\sqrt{20+1} < \\sqrt{20} + \\sqrt{1} $","explain":" <span class='basic_left'> Ta c\u00f3: $\\sqrt{20+1} = \\sqrt{21} < \\sqrt{25} = 5,$ <br\/> m\u00e0 $5 = 4 + 1 = \\sqrt{16} + \\sqrt{1} < \\sqrt{20} + \\sqrt{1} $ <br\/> $\\Rightarrow \\sqrt{20+1} < \\sqrt{20} + \\sqrt{1}$ <br\/> T\u01b0\u01a1ng t\u1ef1: $\\sqrt{40+2} < \\sqrt{40} + \\sqrt{2} \\\\ \\sqrt{60+3} < \\sqrt{60} + \\sqrt{3}$ <br\/> Suy ra $A = \\sqrt{20+1} + \\sqrt{40+2} + \\sqrt{60+3} \\\\ < \\sqrt{20} + \\sqrt{1} + \\sqrt{40} + \\sqrt{2} + \\sqrt{60} + \\sqrt{3} \\\\ = (\\sqrt{1} + \\sqrt{2} + \\sqrt{3}) + (\\sqrt{20} + \\sqrt{40} + \\sqrt{60}) = B$ <br\/> V\u1eady A < B <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":3}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:48"},{"id":"492","post_id":"1021","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":"<center><img src='img\/2.jpg' \/><\/center> T\u00ednh $\\sqrt{1 + 2 + ... +(n - 1) + n + (n - 1) + ... + 2 + 1}$ <br\/> (v\u1edbi $n \\in \\mathbb{N^{*}}$) ","select":["A. $n$ ","B. $2n$","C. $n^{2}$","D. $n+ 1$"],"hint":"S\u1eed d\u1ee5ng: $1 + 2 + 3 + ... + (n - 1) + n = \\dfrac{n(n+1)}{2} $","explain":" Ta c\u00f3: $\\sqrt{1 + 2 + ... +(n - 1) + n + (n - 1) + ... + 2 + 1} \\\\ = \\sqrt{2[1 + 2 + 3 + ... + (n - 1)] + n} \\\\ = \\sqrt{2[1 + 2 + 3 + ... + (n - 1) + n] - n} \\\\ = \\sqrt{2.\\dfrac{n(n+1)}{2} - n} \\\\ = \\sqrt{n(n+1) - n} \\\\ = \\sqrt{n^{2}+n-n} \\\\ = \\sqrt{n^{2}} \\\\ = n$ <span class='basic_left'> <b> Nh\u1eadn x\u00e9t <\/b> <br\/> T\u00ednh t\u1ed5ng c\u1ee7a d\u00e3y s\u1ed1 c\u00e1ch \u0111\u1ec1u: <br\/> T\u1ed5ng = $\\dfrac{\\text{[(s\u1ed1 \u0111\u1ea7u + s\u1ed1 cu\u1ed1i).s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 h\u1ea1ng]}}{\\text{2}}$ <\/span> <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 09:22:48"},{"id":"493","post_id":"1021","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":" C\u00f3 hay kh\u00f4ng gi\u00e1 tr\u1ecb c\u1ee7a $x$ th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n sau: <br\/> $2016.\\sqrt{(1+x)^{2}} + $ $2017.\\sqrt{(1-x)^{2}} = 0$ ? ","select":["C\u00f3 ","Kh\u00f4ng "],"hint":"S\u1eed s\u1ee5ng $\\sqrt{x} \\geq 0$ v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a $x$. ","explain":" <span class='basic_left'> V\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a $x$ ta c\u00f3: <br\/> $2016.\\sqrt{(1+x)^{2}} \\geq 0$ v\u00e0 $2017.\\sqrt{(1-x)^{2}} \\geq 0$ <br\/> Do \u0111\u00f3 $2016.\\sqrt{(1+x)^{2}} + 2017.\\sqrt{(1-x)^{2}} = 0$ <br\/> $\\Leftrightarrow \\begin{cases} 2016.\\sqrt{(1+x)^{2}} = 0 \\\\ 2017.\\sqrt{(1-x)^{2}} = 0 \\end{cases} $ <br\/> $\\Leftrightarrow \\begin{cases} 1 + x = 0 \\\\ 1- x = 0 \\end{cases} $ <br\/> $\\Leftrightarrow \\begin{cases} x = -1 \\\\ x = 1 \\end{cases} $ (v\u00f4 l\u00ed) <br\/> V\u1eady kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a $x$ th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u0111\u1ec1 b\u00e0i. <span class='basic_left'> <b> Nh\u1eadn x\u00e9t: <\/b> <br\/> VT = $2016.\\sqrt{(1+x)^{2}} + 2017.\\sqrt{(1-x)^{2}} > 0$ v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a $x$. <\/span><br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n l\u00e0 Kh\u00f4ng. <\/span><\/span> ","column":2}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:22:48"}]}