\(\left(x-7\right)^{35}=\left(x-7\right)^{25}\)
\(\Leftrightarrow\left(x-7\right)^{35}-\left(x-7\right)^{25}=0\)
\(\Leftrightarrow\left(x-7\right)^{25}\left(\left(x-7\right)^{10}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-7\right)^{25}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\\left[{}\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)
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