\(x^2+y^2+z^2=4x-2y+6z-14\Leftrightarrow x^2-4x+y^2+2y+z^2-6z+14=0\Leftrightarrow\left(x^2-4x+4\right)+\left(y^2+2y+1\right)+\left(z^2-6z+9\right)=0\Leftrightarrow\left(x-2\right)^2+\left(y+1\right)^2+\left(z-3\right)^2=0matkhac:\left\{{}\begin{matrix}\left(x-2\right)^2\ge0\\\left(y+1\right)^2\ge0\\\left(z-3\right)^2\ge0\end{matrix}\right.\Rightarrow\left(x-2\right)^2+\left(y+1\right)^2+\left(z-3\right)^2\ge0mà:\left(x-2\right)^2+\left(y+1\right)^2+\left(z-3\right)^2=0\Rightarrow\left\{{}\begin{matrix}\left(x-2\right)^2=0\\\left(y+1\right)^2=0\\\left(z-3\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\y+1=0\\z-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-1\\z=3\end{matrix}\right..Vậy:x=2;y=-1;z=3\)
