\(\left(x-3\right)^{10}=\left(x-3\right)^{30}\)
\(\Leftrightarrow\left(x-3\right)^{30}-\left(x-3\right)^{10}=0\)
\(\Leftrightarrow\left(x-3\right)^{10}.\left[\left(x-3\right)^{20}-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-3\right)^{10}=0\\\left(x-3\right)^{20}-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\\left[{}\begin{matrix}x-3=1\\x-3=-1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\\\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\end{matrix}\right.\)
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