a, \(5x^2-4\left(x^2-2x+1\right)-5=0\)
\(\Rightarrow5x^2-4x^2+8x-4-5=0\)
\(\Rightarrow x^2-x+9x-9=0\)
\(\Rightarrow x\left(x-1\right)+9\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x+9\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-9\end{matrix}\right.\)
b, \(\left(x^2-9\right)^2-\left(x-3\right)^2=0\)
\(\Rightarrow\left(x^2-9-x+3\right)\left(x^2-9+x-3\right)=0\)
\(\Rightarrow\left(x^2-x-6\right)\left(x^2+x-12\right)=0\)
\(\Rightarrow\left(x^2-3x+2x-6\right)\left(x^2+4x-3x-12\right)=0\)
\(\Rightarrow\left[x\left(x-3\right)+2\left(x-3\right)\right]\left[x\left(x+4\right)-3\left(x+4\right)\right]=0\)
\(\Rightarrow\left(x-3\right)\left(x+2\right)\left(x+4\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=-4\end{matrix}\right.\)
c, \(x^3-3x+2=0\)
\(\Rightarrow x^3+2x^2-2x^2-4x+x+2=0\)
\(\Rightarrow x^2\left(x+2\right)-2x\left(x+2\right)+\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x^2-2x+1\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x-1\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
