\(2012.\left|x-2011\right|+\left(x-2011\right)^2=2013\left|2011-x\right|\)

\(2012.\left|x-2011\right|+\left|x-2011\right|^2=2013\left|x-2011\right|\)

\(\left|x-2011\right|\left(2012+\left|x-2011\right|\right)=2013\left|x-2011\right|\)

\(\Rightarrow2012+\left|x-2011\right|=2013\)

\(\left|x-2011\right|=1\)

\(\Rightarrow\orbr{\begin{cases}x=2012\\x=-2010\end{cases}}\)

Ta có: \(\frac{x+4}{2010}+\frac{x+3}{2011}=\frac{x+2}{2012}+\frac{x+1}{2013}\) 

\(\Rightarrow\left(\frac{x+4}{2010}+1\right)+\left(\frac{x+3}{2011}+1\right)=\left(\frac{x+2}{2012}+1\right)+\left(\frac{x+1}{2013}+1\right)\)

\(\Rightarrow\left(x+2014\right)\left(\frac{1}{2010}+\frac{1}{2011}-\frac{1}{2012}-\frac{1}{2013}\right)=0\)

\(\Rightarrow x=-2014\)

=>2012|x-2011|-|x-2011|+(x-2011)^2+2013>0

=>2011|x-2011|+(x-2011)^2+2013>0(luôn đúng)

a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)

\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)

\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)

\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\)    (1)

Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)

Nên biểu thức (1) xảy ra khi \(x+2013=0\)

\(x=-2013\)

b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)  (2)

Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)

Nên biểu thức (2) xảy ra khi \(x-2011=0\)

\(x=2011\)

ủng hộ mình lên 280 điểm với các bạn

tên níck của bạn đáng ra là kawaii chứ không phải kawai đâu 

Ủng hộ tíck mik nha

Pls đó ~~~

\(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=-3\)

=> \(\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=-3+3\)

=> \(\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}=0\)

=> \(\left(x+2014\right).\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=0\)

Do \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\ne0\)

=> x + 2014 = 0

=> x = -2014