\(ĐKXĐ:\left\{{}\begin{matrix}x\ge0\\y\ge1\\z\ge2\end{matrix}\right.\)
\(pt\Leftrightarrow2\sqrt{x}+2\sqrt{y-1}+2\sqrt{z-2}=x+y+z\)
\(\Leftrightarrow x-2\sqrt{x}+1+\left(y-1\right)-2\sqrt{y-2}+1+\left(z-2\right)-2\sqrt{z-2}+1=0\)
\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-1\right)^2+\left(\sqrt{z-2}-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x}-1\right)^2=0\\\left(\sqrt{y-1}-1\right)^2=0\\\left(\sqrt{z-2}-1\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\\z=3\end{matrix}\right.\left(TM\right)\)
