\(\Leftrightarrow\left(4x+y+z-4\sqrt{xy}-4\sqrt{yz}+\sqrt{zx}\right)+\left(y-6\sqrt{y}+9\right)+\left(z-10\sqrt{z}+25\right)=0\)
\(\Leftrightarrow\left(2\sqrt{x}-\sqrt{y}-\sqrt{z}\right)^2+\left(\sqrt{y}-3\right)^2+\left(\sqrt{z}-5\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2\sqrt{x}-\sqrt{y}-\sqrt{z}=0\\\sqrt{y}-3=0\\\sqrt{z}-5=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=16\\y=9\\z=25\end{matrix}\right.\)
\(\Rightarrow M=3\)
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