\(\left(x-2017\right)^{x+6}-\left(x-2017\right)^{x+2016}=0\)
\(\left(x-2017\right)^{x+6}-\left(x-2017\right)^{x+6+2010}=0\)
\(\left(x-2017\right)^{x+6}-\left(x-2017\right)^{x+6}.\left(x-2017\right)^{2010}=0\)
\(\left(x-2017\right)^{x+6}.\left[1-\left(x-2017\right)^{2010}\right]=0\)
\(TH1:\)
\(\left(x-2017\right)^{x+6}=0\)
\(x-2017=0\)
\(x=0+2017\)
\(x=2017(T/M)\)
\(TH2:\)
\(1-\left(x-2017\right)^{2010}=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2017=1\\x-2017=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1+2017\\x=-1+2017\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2018\\x=2016\end{matrix}\right.\)
Vậy \(x\in\left\{2016;2017;2018\right\}\)
\(\Leftrightarrow\left(x-2017\right)^{x+6}\left[1-\left(x-2017\right)^{10}\right]=0\)
=>(x-2017)(x-2018)(x-2016)=0
hay \(x\in\left\{2017;2018;2016\right\}\)