Ta có \sqrt{1+4 x^{2}}+\sqrt{4 x} \leq \sqrt{2 \cdot(2 x+1)^{2}}=\sqrt{2} \cdot(2 x+1)
Tương tự \sqrt{1+4 y^{2}}+\sqrt{4 y} \leq \sqrt{2} \cdot(2 y+1)
\sqrt{x}+\sqrt{y} \leq \sqrt{2(x+y)} \leq \sqrt{2}
\Rightarrow A \leq \sqrt{2}(2 x+2 y+2)+\sqrt{2} \leq 4 \sqrt{2}+\sqrt{2}=5 \sqrt{2}
Dấu =...