WakeUp wrote: Determine all positive real numbers $x$ and $y$ satisfying the equation \[x+y+\frac{1}{x}+\frac{1}{y}+4=2\cdot (\sqrt{2x+1}+\sqrt{2y+1})\] The equality is equivalent to : $ \frac{(x-\sqrt{2x+1})^2}{x}+\frac{(y-\sqrt{2y+1})^2}{y}=0$ The rest is easy.

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