\(\Leftrightarrow\left(x-3\right)^4-3\left(x^2-6x+9+1\right)-1=0\)
\(\Leftrightarrow\left(x-3\right)^4-3\left(x^2-6x+9\right)-3-1=0\)
\(\Leftrightarrow\left(x-3\right)^4-3\left(x-3\right)^2-4=0\)
\(\Leftrightarrow\left(x-3\right)^4+\left(x-3\right)^2-4\left(x-3\right)^2-4=0\)
\(\Leftrightarrow\left(x-3\right)^2\left[\left(x-3\right)^2+1\right]-4\left[\left(x-3\right)^2+1\right]=0\)
\(\Leftrightarrow\left[\left(x-3\right)^2+1\right]\left[\left(x-3\right)^2-4\right]=0\)
\(\Leftrightarrow\left(x-3\right)^2-4=0\) ( do \(\left(x-3\right)^2+1>0\forall x\) )
\(\Leftrightarrow\left(x-3\right)^2=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=2\\x-3=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\) ( TM )
