\(|9y-1|+\left(2x+3\right)^2=0\)

2.So sánh 

a) 

K
Khách

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7 tháng 10 2020

1) Ta có: \(\left|9y-1\right|+\left(2x+3\right)^2=0\)

Mà \(\hept{\begin{cases}\left|9y-1\right|\ge0\\\left(2x+3\right)^2\ge0\end{cases}}\left(\forall x,y\right)\)

=> \(\left|9y-1\right|+\left(2x+3\right)^2\ge0\left(\forall x,y\right)\)

Dấu "=" xảy ra khi: \(\hept{\begin{cases}\left|9y-1\right|=0\\\left(2x+3\right)^2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}9y-1=0\\2x+3=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-\frac{3}{2}\\y=\frac{1}{9}\end{cases}}\)

Vậy \(\hept{\begin{cases}x=-\frac{3}{2}\\y=\frac{1}{9}\end{cases}}\)

7 tháng 10 2020

2)

a) Ta có: \(\left[\left(-\frac{1}{3}\right)^7\right]^4=\left(\frac{1}{3}\right)^{28}=\frac{1}{3^{28}}\)

và \(\left[\left(-\frac{1}{2}\right)^{14}\right]^2=\left(\frac{1}{2}\right)^{28}=\frac{1}{2^{28}}\)

Vì \(\frac{1}{3^{28}}< \frac{1}{2^{28}}\Rightarrow\left[\left(-\frac{1}{3}\right)^7\right]^4< \left[\left(-\frac{1}{2}\right)^{14}\right]^2\)

b) Ta có: \(\left(-\frac{2}{3}\right)^{12}=\left[\left(-\frac{2}{3}\right)^2\right]^6=\left(\frac{4}{9}\right)^6\)

Ta thấy \(0< \frac{4}{9}< 1\)\(\Rightarrow\left(\frac{4}{9}\right)^6>\left(\frac{4}{9}\right)^7\)

\(\Rightarrow\left(-\frac{2}{3}\right)^{12}>\left(\frac{4}{9}\right)^7\)

25 tháng 7 2017

\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)

\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)

\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)

\(=3-\left(-1\right)\)

\(=4\)

b)   \(=\left(\frac{1}{4}+\frac{25}{2}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right)\)

       \(=\left(\frac{4}{16}+\frac{200}{16}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3.3}{2.3.4}-\frac{2}{2.3.4}\right)\right)\)

     \(=\left(\frac{199}{16}\right):\left(12-\frac{7}{12}:\left(\frac{9}{24}-\frac{2}{24}\right)\right)\)

      \(=\frac{199}{16}:\left(12-\frac{7}{12}.\frac{24}{7}\right)\)

    \(=\frac{199}{16}:\left(12-2\right)\)

\(=\frac{199}{16}:10\)

\(=\frac{199}{160}\)

c)   \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)

\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)

\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)

\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)

\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)

     

25 tháng 7 2017

giờ mk phải đi ngủ r mai mk làm cho 

9 tháng 7 2019

\(A=\frac{99}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{99.100}\right)\)

\(A=\frac{99}{100}-\left(1-\frac{1}{100}\right)\)

\(A=\frac{99}{100}-\frac{99}{100}\)

\(A=\frac{99-99}{100}=0\)

Bài 2 

\(\left(3x+5\right).\left(2x-4\right)=0\)

\(TH1:3x+5=0\)

\(3x=-5\)

\(x=-\frac{5}{3}\)

\(TH2:2x-4=0\)

\(2x=4\)

\(x=2\)

\(\left(x^2-1\right).\left(x+3\right)=0\)

\(\Rightarrow x^2-1=0\)

\(x^2=1\)

\(\Rightarrow x=1\)

\(x+3=0\)

\(x=-3\)

\(5x^2-\frac{1}{2}x=0\)

\(\Rightarrow5x^2-\frac{x}{2}=0\)

\(\Rightarrow5x^2=\frac{5x^2}{1}=\frac{5x^2.2}{2}\)

\(10x^2-x=x.\left(10x-1\right)\)

\(\frac{x.\left(10x-1\right)}{2}=0\)

\(\frac{x.\left(10x-1\right)}{2}.2=0.2\)

\(10x-1=0\)

\(x=\frac{1}{10}=0.100\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{10}=0.100\\x=0\end{cases}}\)

\(\frac{x}{4}-\frac{1}{2}=\frac{3}{4}\)

\(\frac{x}{4}=\frac{3}{4}+\frac{1}{2}\)

\(\frac{x}{4}=\frac{5}{4}\)

\(\Rightarrow x=5\)

\(\frac{1}{8}+\frac{7}{8}:x=\frac{3}{4}\)

\(\frac{7}{8}:x=\frac{3}{4}-\frac{1}{8}\)

\(x=\frac{7}{8}:\frac{5}{8}\)

\(x=\frac{56}{40}=\frac{28}{20}=\frac{14}{10}=\frac{7}{5}\)

26 tháng 10 2016

a ) \(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}+\frac{1}{2}=-4\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}=-4-\frac{1}{2}\)

     \(\left(\frac{2}{5}-x\right):\frac{4}{3}=-\frac{9}{2}\)

        \(\frac{2}{5}-x=-\frac{9}{2}.\frac{4}{3}\)

        \(\frac{2}{5}-x=-3\)

                   \(x=\frac{2}{5}-\left(-3\right)\)

                   \(x=\frac{2}{5}+3\)

                   \(x=\frac{3}{5}-\frac{15}{5}\)

                   \(x=-\frac{12}{5}\)

Vay \(x=-\frac{12}{5}\) 

    

  

26 tháng 10 2016

b ) \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(1+\frac{2}{5}+\frac{2}{3}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(\frac{15}{15}+\frac{6}{15}+\frac{10}{15}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\left(\frac{15+6+10}{15}\right)=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right):\frac{31}{15}=-\frac{5}{4}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right)=-\frac{5}{4}.\frac{31}{15}\)

     \(\left(-3+\frac{3}{x}-\frac{1}{3}\right)=-\frac{1}{4}.\frac{31}{3}\)

        \(-3+\frac{3}{x}-\frac{1}{3}=-\frac{31}{12}\)

        \(-3+\frac{3}{x}=-\frac{31}{12}+\frac{1}{2}\)

        \(-3+\frac{3}{x}=-\frac{31}{12}+\frac{6}{12}\)

        \(-3+\frac{3}{x}=\frac{-25}{12}\)

                     \(\frac{3}{x}=\frac{-25}{12}+3\)

                      \(\frac{3}{x}=\frac{-25}{12}+\frac{36}{12}\)

                      \(\frac{3}{x}=\frac{5}{6}\)

                      \(\frac{18}{6x}=\frac{5x}{6x}\)

Đèn dây , bạn tự làm tiếp nhé , de rồi chứ

Bài 1:...
Đọc tiếp

Bài 1: Tính

a. \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)+\left(1+\frac{1}{4\cdot6}\right).....\left(1+\frac{1}{99\cdot101}\right)\)

b. \(\left[\sqrt{0,64}+\sqrt{0,0001}-\sqrt{\left(-0,5\right)^2}\right]\div\left[3\cdot\sqrt{\left(0,04\right)^2}-\sqrt{\left(-2\right)^4}\right]\)

c. \(\frac{5.4^{15}\cdot9^9-4.3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot6^{15}-7\cdot6^{10}\cdot2^{20}\cdot3^6}{9\cdot6^{19}\cdot2^9-4\cdot3^{17}\cdot2^{26}}+0,\left(6\right)\)

Bài 2: Tìm x, y, z biết :
a. \(\left(x-10\right)^{1+x}=\left(x-10\right)^{x+2009}\left(x\in Z\right)\)

b. \(\left|x-2007\right|+\left|x-2008\right|+\left|y-2009\right|+\left|x-2010\right|=3\left(x,y\in N\right)\) 

c. \(25-y^2=8\left(x-2009\right)^2\left(x,y\in Z\right)\)

d. \(2008\left(x-4\right)^2+2009\left|x^2-16\right|+\left(y+1\right)^2\le0\)

e. \(2x=3y\) ; \(4z=5x\) và \(3y^2-z^2=-33\)

Bài 3: Chứng minh rằng

a. \(1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{2009^2}>\frac{1}{2009}\)

b. \(\left[75\cdot\left(4^{2008}+4^{2007}+4^{2006}+...+4+1\right)+25\right]⋮100\)

Bài 4: 

a. Tìm giá trị nhỏ nhất của biểu thức : \(M=\left(x^2+2\right)+\left|x+y-2009\right|+2005\)

b. So sánh: \(31^{11}\) và \(\left(-17\right)^{14}\)

c. So sánh: \(\left(\frac{9}{11}-0,81\right)^{2012}\) và \(\frac{1}{10^{4024}}\)

1

Bài 1 :\(a,=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{100^2}{99.101}\)

           \(=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4...101}\)

          \(=100.\frac{2}{101}=\frac{200}{101}\)

26 tháng 6 2018

Bài 1 và Bài 2 dễ, bn có thể tự làm được!

Bài 3:

a) ta có: 1020 = (102)10 = 10010

=> 10010>910

=> 1020>910

b) ta có: (-5)30 = 530 =( 53)10 = 12510 ( vì là lũy thừa bậc chẵn)

(-3)50 = 350 = (35)10= 24310

=> 12510 < 24310

=> (-5)30 < (-3)50

c) ta có: 648 = (26)8= 248

1612 = ( 24)12 = 248

=> 648 = 1612

d) ta có: \(\left(\frac{1}{16}\right)^{10}=\left(\frac{1}{2^4}\right)^{10}=\frac{1}{2^{40}}\)

\(\left(\frac{1}{2}\right)^{50}=\frac{1}{2^{50}}\)

\(\Rightarrow\frac{1}{2^{40}}>\frac{1}{2^{50}}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)

26 tháng 6 2018

3.a) Ta có: 910=(32)10=320

Mà 1020<320

Nên 1020<910

c)Ta có:648 =(82)8=816

1612=(23)12=836

vì 816<836

Nên 648<162

              

12 tháng 7 2019

a)\(\left(\frac{1}{3}\right)^{-1}-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^4.2^3=3-1+\frac{1}{16}.8=3-1+\frac{1}{2}=\frac{5}{2}\\ \)

b)\(2^2.2^3.\left(\frac{2}{3}\right)^{-2}=2^5.\frac{9}{4}=72\)

c)\(\left(\frac{4}{3}\right)^{-2}.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^5:\left(\frac{3}{2}\right)^3=\frac{9}{128}\)

2)

\(3^{x+1}=9^x\Leftrightarrow3^x.3=9^x\Rightarrow3=9^x:3^x\Rightarrow3=3^x\Rightarrow x=1\)

\(\left(x-0,1\right)^2=6,25\Leftrightarrow\left(x-0,1\right)^2=2,5^2\Rightarrow\left(x-0,1\right)=2,5\Rightarrow x=2,5+0,1=2,6\)

\(3^{2x-1}=243\Leftrightarrow3^{2x-1}=3^5\Rightarrow2x-1=5\Rightarrow2x=6\Rightarrow x=3\)

\(\left(4x-3\right)^4=\left(4x-3\right)^2\Rightarrow x=1\)