BALTIC-WAY 2000 Problem 18

Determine all positive real numbers $x$ and $y$ satisfying the equation

$x+y+\frac{1}{x}+\frac{1}{y}+4=2 \cdot(\sqrt{2 x+1}+\sqrt{2 y+1}) .$

Dataset text NuminaMath olympiads. Quoted with source.

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x=y=1+\sqrt{2}

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