\(\Leftrightarrow x+y=\sqrt{x+10}+\sqrt{y+10}\le\sqrt{2\left(x+y+20\right)}\) (\(x+y>0\))
\(\Rightarrow\left(x+y\right)^2\le2\left(x+y+20\right)\)
\(\Rightarrow\left(x+y\right)^2-2\left(x+y\right)-40\le0\)
\(\Rightarrow\left(x+y+1+\sqrt{41}\right)\left(x+y-1-\sqrt{41}\right)\le0\)
\(\Rightarrow x+y-1-\sqrt{41}\le0\)
\(\Rightarrow x+y\le1+\sqrt{41}\)
Dấu "=" xảy ra khi \(x=y=\frac{1+\sqrt{41}}{2}\)
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