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1997 USAMO Problems/Problem 5

Revision as of 09:38, 1 July 2011 by Mcqueen (talk | contribs) (Created page with "== Problem == Prove that, for all positive real numbers <math>a, b, c,</math> <math>(a^3+b^3+abc)^{-1}+(b^3+c^3+abc)^{-1}+(a^3+c^3+abc)^{-1}\le(abc)^{-1}</math>. == Solution ==")

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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

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