\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)
\(\Rightarrow\left(x-1\right)^{x+6}-\left(x-1\right)^{x+2}=0\)
\(\Rightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^4-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^{x+2}=0\\\left(x-1\right)^4=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-1=1\\x-1=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)
( x-1 )\(^{x+2}\) = ( x-1 )\(^{x+6}\)
\(\Rightarrow\) (x-1)\(^{x+6}\) : (x-1)\(^{x+2}\) = 1
(x-1)\(^4\) = 1
(x-1) = \(\pm\) 1
+ ) (x-1) = 1 \(\Rightarrow\) x = 2
+) (x-1) = -1 \(\Rightarrow\) x = 0
vậy x = \(\left\{0;2\right\}\)
