\(x^3-4x^2-9x+36=0\)
=> \(x^2\left(x-4\right)-9\left(x-4\right)=0\)
=> \(\left(x-4\right)\left(x^2-9\right)=0\)
=> \(\orbr{\begin{cases}x-4=0\\x^2-9=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=\pm3\end{cases}}\)
\(\left(x^2-9\right)^2-\left(x-3\right)^2=0\)
=> \(\left(x^2-9+x-3\right)\left[x^2-9-\left(x-3\right)\right]=0\)
=> \(\left(x^2+x-12\right)\left(x^2-9-x+3\right)=0\)
=> \(\left(x^2+x-12\right)\left(x^2-x-6\right)=0\)
=> \(\left(x^2-3x+4x-12\right)\left(x^2+2x-3x-6\right)=0\)
=> \(\left[x\left(x-3\right)+4\left(x-3\right)\right]\left[x\left(x+2\right)-3\left(x+2\right)\right]=0\)
=> \(\left(x-3\right)\left(x+4\right)\left(x-3\right)\left(x+2\right)=0\)
=> \(\left(x-3\right)^2\left(x+4\right)\left(x+2\right)=0\)
=> \(\hept{\begin{cases}\left(x-3\right)^2=0\\x+4=0\\x+2=0\end{cases}}\Rightarrow\hept{\begin{cases}x=3\\x=-4\\x=-2\end{cases}}\)
\(x^3-3x+2=0\)
=> \(x^3-x-2x+2=0\)
=> \(x^2\left(x-1\right)-2\left(x-1\right)=0\)
=> \(\left(x-1\right)\left(x^2-2\right)=0\)
=> x = 1
