\(x^2+2x-2=0\Rightarrow\left\{{}\begin{matrix}x^2+2x+1=3\\x^2=2-2x\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left(x+1\right)^2=3\\x^4=\left(2-2x\right)^2=4x^2-8x+4\end{matrix}\right.\)
Thay vào M ta được:
\(M=x^4+16x+2017=4x^2-8x+4+16x+2017\)
\(\Rightarrow M=4x^4+8x+4+2017=4\left(x^2+2x+1\right)+2017\)
\(\Rightarrow M=4\left(x+1\right)^2+2017=4.3+2017=2029\)
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