\(\left(x^2-5x+8\right)^2-\left(5x-17\right)^2=0\)
\(\Leftrightarrow\left(x^2-5x+8-5x+17\right)\left(x^2-5x+8+5x-17\right)=0\)
\(\Leftrightarrow\left(x^2-10x+25\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left(x^2-5x-5x+25\right)\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[x\left(x-5\right)-5\left(x-5\right)\right]\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-5\right)^2.\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-5\right)^2=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\\x=-3\end{matrix}\right.\)
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