Chứng minh rằng với mọi số nguyên dương k" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">k${\displaystyle k}$ ; ta có đẳng thức :

$$\frac{1}{{\sin }^2\frac{\pi }{4k+2}}+\frac{1}{{\sin }^2\frac{3\pi }{4k+2}}+\frac{1}{{\sin }^2\frac{5\pi }{4k+2}}+\cdots +\frac{1}{{\sin }^2\frac{(2k-1)\pi }{4k+2}}=2k(k+1$$ 

Tìm x,y,z \(\in\) N*

x7+y11+z13=0,(946053)${\displaystyle \frac{x}{7}+\frac{y}{11}+\frac{z}{13}=0,(946053)}$

Thực hiện phép tính

25+15.(−34)=35.(−34)" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">25+15.(−34)=35.(−34)${\displaystyle \frac{2}{5}}+{\displaystyle \frac{1}{5}}.\left({\displaystyle \frac{-3}{4}}\right)={\displaystyle \frac{3}{5}}.\left({\displaystyle \frac{-3}{4}}\right)$

34−0,25)−(312−112)" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">(−3)2.(34−0,25)−(312−112)

Bài 1: Tìm $x$, biết:

1024. a) |x−3|=5x+8" role="presentation" style="border:0px; box-sizing:inherit; direction:ltr; display:inline-block; float:none; font-size:18.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">12−|x−3|=5x+8$12-|x-3|=5x+8$                                                                         
1025. b) (x+3)10=1024.1252.252" role="presentation" style="border:0px; box-sizing:inherit; direction:ltr; display:inline-table; float:none; font-size:18.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">(√x+3)10=1024.1252.252${\left(\sqrt{x}+3\right)}^{10}={1024.125}^2{.25}^2$
1026. c) $\frac{3-0,2x}{5}=\frac{7}{15}+1,4x$                                         
1027. d) (6427)x=4.59.710−511.79359.4" role="presentation" style="border:0px; box-sizing:inherit; direction:ltr; display:inline-block; float:none; font-size:18.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">(6427)x=4.59.710−511.79359.4

Bài 2: Tính

A = 123.1212.5−224.33752.114−302.115" role="presentation" style="border:0px; box-sizing:inherit; direction:ltr; display:inline-block; float:none; font-size:18.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">123.1212.5−224.33752.114−302.115$\frac{{12}^3{.121}^2.5-{22}^4{.3}^3}{{75}^2{.11}^4-{30}^2{.11}^5}$

B = $5\frac{11}{18}+\left(4\frac{1}{5}-3\frac{2}{9}\right)-\left(13\frac{1}{15}-\frac{2}{3}+\frac{7}{18}\right)+\left(\frac{2}{3}.\sqrt{2}-\sqrt{\frac{8}{9}}\right)$

$Bài\; 3:\; Tìm\; x\; biết:$

1. a) |x−2|=|2x+1|" role="presentation" style="border:0px; box-sizing:inherit; direction:ltr; display:inline-block; float:none; font-size:18.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">|x−2|=|2x+1|$|x-2|=|2x+1|$                                                                       
2. b) $3\left(x+\frac{1}{2}\right)-\frac{1}{2}\left(4x-\frac{2}{3}\right)=\frac{5}{6}$
3. c) $\frac{7x+1}{4}=\frac{2x-9}{3}$

$1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}$

$\sqrt{\frac{25}{81}}:2\frac{2}{5}-4\frac{5}{9}:2\frac{2}{5}$

$6.{\left(-\frac{-1}{2}\right)}^2+\frac{3}{5}$

$1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}$

$\sqrt{\frac{25}{81}}:2\frac{2}{5}-4\frac{5}{9}:2\frac{2}{5}$

$6.{\left(-\frac{-1}{2}\right)}^2+\frac{3}{5}$

a) &#x2212;15&lt;11000" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">−15<11000$\frac{-1}{5}<\frac{1}{1000}$                            

b) 267&#x2212;268&gt;&#x2212;13471343" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">267−268>−13471343$\frac{267}{-268}>\frac{-1347}{1343}$

c) &#x2212;1338&lt;29&#x2212;88" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">−1338<29−88$\frac{-13}{38}<\frac{29}{-88}$

d) &#x2212;1831=&#x2212;181818313131" role="presentation" style="border:0px; direction:ltr; display:inline-table; float:none; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">−1831=−181818313131

So sánh \(A=\frac{2^{2016}+7}{2^{2014}+7}\)và \(B=\frac{2^{2013}+1}{2^{2011}+1}\)

Cho a,b&#x2208;R;n&#x2208;N&#x2217;" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvetica,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a,b∈R;n∈N∗${\displaystyle a,b\in R;n\in N^{\ast }}$. Chứng minh rằng:

cho a,b,c là các số dường thỏa mãn :

1a+1b+1c" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:18.08px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a+b+c≥1a+1b+1c$a+b+c\ge {\displaystyle \frac{1}{a}}+{\displaystyle \frac{1}{b}}+{\displaystyle \frac{1}{c}}$ CMR:

ab+bc+ca&#x2265;1ab+1bc+1ac" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.08px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a b+bc+ca≥1ab+1bc+1ac

ab+bc+ca&#x2265;1ab+1bc+1ac" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.08px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">giúp mình với nha