\(Đk:x\ge5;y\ge2019;z\ge-2021\)
\(\sqrt{x-5}+\sqrt{y-2019}+\sqrt{z+2021}=\dfrac{1}{2}\left(x+y+z\right)\)
\(\Leftrightarrow x+y+z-2\sqrt{x-5}-2\sqrt{y-2019}-2\sqrt{z+2021}=0\)
\(\Leftrightarrow\left[\left(x-5\right)-2\sqrt{x-5}+1\right]+4+\left[\left(y-2019\right)-2\sqrt{y-2019}+1\right]+2018+\left[\left(z+2021\right)-2\sqrt{z+2021}+1\right]-2022=0\)
\(\Leftrightarrow\left(\sqrt{x-5}-1\right)^2+\left(\sqrt{y-2019}-1\right)^2+\left(\sqrt{z+2021}-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x-5}-1\right)^2=0\\\left(\sqrt{y-2019}-1\right)^2=0\\\left(\sqrt{z+2021}-1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=2020\\z=-2020\end{matrix}\right.\left(nhận\right)\)
