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sum of squares = 1 kind of ineq

Source: Tuymaada, Day 2, Problem 8

July 30, 2005
inequalitiesinequalities proposed

Problem Statement

Let a,b,ca,b,c be positive reals s.t. a2+b2+c2=1a^2+b^2+c^2=1. Prove the following inequality ∑aa3+bc>3. \sum \frac{a}{a^3+bc} >3 .
Proposed by A. Khrabrov
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