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Not too difficult

Source: JbMO 2004, PROBLEM 1

July 20, 2004
inequalitiesanalytic geometrycalculusinequalities proposedalgebra

Problem Statement

Prove that the inequality x+yx2−xy+y2≤22x2+y2 \frac{ x+y}{x^2-xy+y^2 } \leq \frac{ 2\sqrt 2 }{\sqrt{ x^2 +y^2 } } holds for all real numbers xx and yy, not both equal to 0.
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