\(M+2019=2xy-yz-zx+2020\)
\(=2xy-yz-zx+x^2+y^2+z^2\)
\(=\left(x+y-\frac{z}{2}\right)^2+\frac{3z^2}{4}\ge0\)
\(\Rightarrow M_{min}=0\) khi \(\left\{{}\begin{matrix}x+y-\frac{z}{2}=0\\\frac{3z^2}{4}=0\\x^2+y^2+z^2=2020\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\z=0\\x^2+y^2=2020\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\pm\sqrt{1010}\\y=-x\\z=0\end{matrix}\right.\)
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