(|x|-2011)^ (2+2008)×(2+2009)=-(2^3-3^2)^2009
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Ta có
(|x|-2011)^(n+2008)(n+2009)=-(-355)^2009=355 ^2009
n+2008 và n+2009 là 2 số nguyên liên tiếp => (n+2009)(n+2008) là số chẵn => (|x|-2011)^(n+2008)(n+2009) là số chính phương
=> 355 ^2009 là số chính phương mà 355^2009=5^2009 x 71^2009
5,7 là số nguyên tố
=> 2009 là số lẻ (vô lý)
Không có x t/m
(Có gì mắc bạn nhắn mình giải đáp cho)
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(2008 x 2009 x 2010 x 2011) x (1 + 1/2 : 3/2 - 4/3)
=(2008 x 2009 x 2010 x 2011) x (1 + 1/3 - 4/3)
=(2008 x 2009 x 2010 x 2011) x (4/3 - 4/3)
=(2008 x 2009 x 2010 x 2011) x 0
=0
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\(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}=\frac{x-4}{2008}\)
\(\Rightarrow\left(\frac{x-1}{2011}+1\right)+\left(\frac{x-2}{2010}+1\right)-\left(\frac{x-3}{2009}+1\right)=\frac{x-4}{2008}+1\)
\(\Rightarrow\frac{x-1+2011}{2011}+\frac{x-2+2010}{2010}-\frac{x-3+2009}{2009}=\frac{x-4+2008}{2008}\)
\(\Rightarrow\frac{x-2012}{2011}+\frac{x-2012}{2010}-\frac{x-2012}{2009}=\frac{x-2012}{2008}\)
\(\Rightarrow\frac{x-2012}{2011}+\frac{x-2012}{2010}-\frac{x-2012}{2009}-\frac{x-2012}{2008}=0\)
\(\Rightarrow\left(x-2012\right)\left(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)
Mà \(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\ne0\)
=> x - 2012 = 0
=> x = 2012
Vậy x = 2012
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\(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}=\frac{x-4}{2008}\)
\(\Rightarrow\left(\frac{x-1}{2011}+1\right)+\left(\frac{x-2}{2010}+1\right)-\left(\frac{x-3}{2009}+1\right)=\frac{x-4}{2008}+1\)
\(\Rightarrow\frac{x-1+2011}{2011}+\frac{x-2+2010}{2010}-\frac{x-3+2009}{2009}=\frac{x-4+2008}{2008}\)
\(\Rightarrow\frac{x-2012}{2011}+\frac{x-2012}{2010}-\frac{x-2012}{2009}=\frac{x-2012}{2008}\)
\(\Rightarrow\frac{x-2012}{2011}+\frac{x-2012}{2010}-\frac{x-2012}{2009}-\frac{x-2012}{2008}=0\)
\(\Rightarrow\left(x-2012\right)\left(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)
Mà \(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\ne0\)
=> x - 2012 = 0
=> x = 2012
Vậy x = 2012
Kết quả đúng òi nhưng mà dấu suy ra thứ 2 ế \(x-1+2011\) thì bằng \(x+2010\) mà. Cả mấy cái bên cạnh cũng bị tính sai.
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\(\frac{2009}{1}+\frac{2010}{2}+...+\frac{5016}{2008-2008}\)
\(=\frac{2009}{1}+\frac{2010}{2}+...+\frac{5016}{0}\)
Sau đó QĐM(bạn tự QĐ nha)
\(=\frac{0}{0}+\frac{0}{0}+...+\frac{5016}{0}\)
\(=\frac{5016}{0}=0\)
\(\Rightarrow\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}\right).x=0\)
Mà \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}\right)\ne0\)
\(\Rightarrow x=0\)
x=2012
\(\left(\left|x\right|-2011\right)^{\left(2+2008\right)}\cdot\left(2+2009\right)=-\left(2^3-3^2\right)^{2009}\)
\(\left(\left|x\right|-2011\right)^{2010}\cdot2011=-\left(8-9\right)^{2009}\)
\(\left(\left|x\right|-2011\right)^{2010}\cdot2011=-\left(-1\right)^{2009}\)
\(\left(\left|x\right|-2011\right)^{2010}\cdot2011=-\left(-1\right)\)
\(\left(\left|x\right|-2011\right)^{2010}\cdot2011=1\)
\(\left(\left|x\right|-2011\right)^{2010}=\dfrac{1}{2011}\)
???