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Two variable inequality

Source: Junior Turkish Mathematical Olympiad 2010 Problem 4

July 24, 2011
inequalitiesrearrangement inequalityinequalities proposed

Problem Statement

Prove that a2b2(a2+b2−2)≥(a+b)(ab−1) a^2b^2(a^2+b^2-2) \geq (a+b)(ab-1) for all positive real numbers aa and b.b.
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