\(x^4-4x^4-4x^2-x^3+4x^2+4x-x^2+4x+4=0\)
\(\Leftrightarrow x^2\left(x^2-4x-4\right)-x\left(x^2-4x-4\right)-\left(x^2-4x-4\right)=0\)
\(\Leftrightarrow\left(x^2-x-1\right)\left(x^2-4x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-4x-4=0\\x^2-x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2+2\sqrt{2}\\x=2-2\sqrt{2}\\x=\frac{1+\sqrt{5}}{2}\\x=\frac{1-\sqrt{5}}{2}\end{matrix}\right.\)
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