Bài 5: ĐKXĐ: x>=2021; y>=2022; z>=2023
Ta có: \(\sqrt{x-2021}+\sqrt{y-2022}+\sqrt{z-2023}=\frac12\left(x+y+z-6063\right)\)
=>\(x+y+z-6063=2\sqrt{x-2021}+2\sqrt{y-2022}+2\sqrt{z-2023}\)
=>\(x-2021-2\sqrt{x-2021}+1+y-2022-2\sqrt{y-2022}+1+z-2023-2\sqrt{z-2023}+1=\) 0
=>\(\left(\sqrt{x-2021}-1\right)^2+\left(\sqrt{y-2022}-1\right)^2+\left(\sqrt{z-2023}-1\right)^2=0\)
=>\(\begin{cases}x-2021=1\\ y-2022=1\\ z-2023=1\end{cases}\Rightarrow\begin{cases}x=2022\\ y=2023\\ z=2024\end{cases}\)
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