1. \(x^4-4x^3+3x^2+4x-4=0\)
\(\Rightarrow x^4-4x^3+4x^2-x^2+4x-4=0\)
\(\Rightarrow x^2\left(x^2-4x+4\right)-\left(x^2-4x+4\right)=0\)
\(\Rightarrow\left(x^2-4x+4\right)\left(x^2-1\right)=0\)
\(\Rightarrow\left(x-2\right)^2\left(x-1\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-1=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=1\\x=-1\end{matrix}\right.\)
2. \(x^2-3x+2=0\)
\(\Rightarrow x^2-2x-x+2=0\)
\(\Rightarrow x\left(x-2\right)-\left(x-2\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
\(2,x^2-3x+2=0\)
\(\Rightarrow x^2-2x-x+2=0\)
\(\Rightarrow\left(x^2-x\right)-\left(2x-x\right)=0\)
\(\Rightarrow x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
