ĐKXĐ: \(0\le x;y\le3\)
Trừ vế cho vế: \(\sqrt{2x}-\sqrt{2y}+\sqrt{3-y}-\sqrt{3-x}=0\)
\(\Leftrightarrow\frac{2\left(x-y\right)}{\sqrt{2x}+\sqrt{2y}}+\frac{x-y}{\sqrt{3-y}+\sqrt{3-x}}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{2}{\sqrt{2x}+\sqrt{2y}}+\frac{1}{\sqrt{3-y}+\sqrt{3-x}}\right)=0\)
\(\Leftrightarrow x=y\)
Thay vào pt đầu: \(\sqrt{2x}+\sqrt{3-x}=m\)
\(\left(\sqrt{2x}+\sqrt{3-x}\right)^2\le\left(2+1\right)\left(x+3-x\right)=9\)
\(\Rightarrow\sqrt{2x}+\sqrt{3-x}\le3\)
\(\sqrt{2x}+\sqrt{3-x}\ge\sqrt{2x+3-x}=\sqrt{3+x}\ge\sqrt{3}\)
\(\Rightarrow\sqrt{3}\le m\le3\) mà m nguyên \(\Rightarrow\left[{}\begin{matrix}m=2\\m=3\end{matrix}\right.\) \(\Rightarrow\sum m=5\)
