ĐKXĐ: \(\left\{{}\begin{matrix}x-1\ge0\\y-3\ge0\\z+1\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge1\\y\ge3\\z\ge-1\end{matrix}\right.\)
\(\sqrt{x-1}+2\sqrt{y-3}+\sqrt{z+1}=\dfrac{1}{2}\left(x+y+z+3\right)\)
\(\Rightarrow2\sqrt{x-1}+2.2\sqrt{y-3}+2\sqrt{z+1}=x+y+z+3\\ \Rightarrow0=\left(x-1-2.\sqrt{x-1}+1\right)+\left(y-3-2.\sqrt{y-3}.2+4\right)+\left(z+1+2\sqrt{z+1}+1\right)\\ \Rightarrow0=\left(\sqrt{x-1}-1\right)^2+\left(\sqrt{y-3}+2\right)^2+\left(\sqrt{z+1}+1\right)^2\)
\(\Rightarrow\left\{{}\begin{matrix}\left(\sqrt{x-1}-1\right)^2=0\\\left(\sqrt{y-3}-2\right)^2=0\\\left(\sqrt{z+1}-1\right)^2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\left(TM\right)\\y=7\left(TM\right)\\z=0\left(TM\right)\end{matrix}\right.\)
