\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\Leftrightarrow\left(x-1\right)^{x+4}-\left(x-1\right)^{x+2}=0\)
\(\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^{x+2}=0\\\left(x-1\right)^2-1=0\end{matrix}\right.\)
+) \(\left(x-1\right)^{x+2}=0\Leftrightarrow x=1\)
+) \(\left(x-1\right)^2-1=0\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)
Vậy x = 1 hoặc x = 2 hoặc x = 0
\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(x+2\ne x+4\)
\(\Rightarrow x-1\in\left\{0;\pm1\right\}\)
\(\Rightarrow\in\left\{0;1;2\right\}\)
