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Given a+b=1; show expression<=1(Well-known)

Source: RMO 2012

December 2, 2012
logarithmsfunctioninequalitiesinequalities unsolved

Problem Statement

Let aa and bb be positive real numbers such that a+b=1a+b=1. Prove that aabb+abba≤1a^ab^b+a^bb^a\le 1.
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