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n variable inequality

Source: IMO Shortlist 2006, Algebra 4, AIMO 2007, TST 7, P1

June 28, 2007
inequalitiesfunctionalgebraIMO Shortlist

Problem Statement

Prove the inequality: \sum_{i < j}{\frac {a_{i}a_{j}}{a_{i} \plus{} a_{j}}}\leq \frac {n}{2(a_{1} \plus{} a_{2} \plus{}\cdots \plus{} a_{n})}\cdot \sum_{i < j}{a_{i}a_{j}} for positive reals a1,a2,…,an a_{1},a_{2},\ldots,a_{n}.
Proposed by Dusan Dukic, Serbia
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