Difference between revisions of "1997 USAMO Problems/Problem 5"

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Revision as of 09:38, 1 July 2011

Problem

Prove that, for all positive real numbers $a, b, c,$

$(a^3+b^3+abc)^{-1}+(b^3+c^3+abc)^{-1}+(a^3+c^3+abc)^{-1}\le(abc)^{-1}$.

Solution