MathDB

(x+y)/2,\sqrt{xy}, 2xy/(x+y),\sqrt{((x^2 +y^2)/2} integers with sum 66

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1995 p2

February 20, 2020

SumIntegersalgebra

Problem Statement

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