\(x^2+y^2+z^2-6x-22y+12z+166=0\)
\(\Leftrightarrow x^2+y^2+z^2-6x-22y+12z+121+9+36=0\)
\(\Leftrightarrow\left(x^2-6x+9\right)+\left(y^2-22y+121\right)+\left(z^2+12z+36\right)=0\)
\(\Leftrightarrow\left(x-3\right)^2+\left(y-11\right)^2+\left(z+6\right)^2=0\)
\(\hept{\begin{cases}\left(x-3\right)^2\ge0\\\left(y-11\right)^2\ge0\\\left(z+6\right)^2\ge0\end{cases}}\Rightarrow\hept{\begin{cases}\left(x-3\right)^2=0\\\left(y-11\right)^2=0\\\left(z+6\right)^2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x-3=0\\y-11=0\\z+6=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=3\\y=11\\z=-6\end{cases}}\)
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