CZ-SK-MO 1995 Problem 2

Find the positive real numbers $x,y$ for which $\frac{x+y}{2},\sqrt{xy},\frac{2xy}{x+y},\sqrt{\frac{x^2 +y^2}{2}}$ are integers whose sum is $66$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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