Question

\(\left(x-5\right)^{2017}=\left(x-5\right)^{2015}\)

Answer 1

\(\left(x-5\right)^{2017}=\left(x-5\right)^{2015}\)

\(\Rightarrow\left(x-5\right)^{2017}-\left(x-5\right)^{2015}=0\)

\(\Rightarrow\left(x-5\right)^{2015}\left[\left(x-5\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^{2015}=0\Rightarrow x-5=0\Rightarrow x=5\\\left[{}\begin{matrix}\left(x-5\right)^2=1\Rightarrow x-5=1\Rightarrow x=6\\x-5=-1\Rightarrow x=4\end{matrix}\right.\end{matrix}\right.\)

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