Ta có:
\(\sqrt{x-2}+\sqrt{4-x}\le\sqrt{2\left(x-2+4-x\right)}=2\)
\(\Rightarrow3x+y+8\le2+2\left(\sqrt{2x+y}+2\sqrt{x+1}\right)\)
\(\Rightarrow\left(2x+y-2\sqrt{2x+y}+1\right)+\left(x+1-4\sqrt{x+1}+4\right)\le0\)
\(\Rightarrow\left(\sqrt{2x+y}-1\right)^2+\left(\sqrt{x+1}-2\right)^2\le0\)
\(\Rightarrow\left\{{}\begin{matrix}\sqrt{2x+y}-1=0\\\sqrt{x+1}-2=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=3\\y=-5\end{matrix}\right.\)
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