Question

Tìm x, biết (x-2)^x+2012-(x-2)^x+2010=0

Answer 1

\(\left(x-2\right)^{x+2012}-\left(x-2\right)^{x+2010}=0\)

\(\Rightarrow\left(x-2\right)^{x+2010}\left[\left(x-2\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^{x+2010}=0\\\left(x-2\right)^2-1=0\end{matrix}\right.\)

+) \(\left(x-2\right)^{x+2010}=0\Rightarrow x-2=0\Rightarrow x=2\)

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

\(\Rightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy \(x\in\left\{2;3;1\right\}\)