\(\left(x-2\right)^5=\left(x-2\right)^{10}\)
\(\Leftrightarrow\left(x-2\right)^5-\left(x-2\right)^{10}=0\)
\(\Leftrightarrow\left(x-2\right)^5\left[1-\left(x-2\right)^5\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^5=0\\1-\left(x-2\right)^5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^5=0\\\left(x-2\right)^5=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-2=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
