1997 USAMO Problems/Problem 5: Difference between revisions

Revision as of 12:33, 4 July 2013

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

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

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

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

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 [[Category:Olympiad Algebra Problems]]
 [[Category:Olympiad Inequality Problems]]
+{{MAA Notice}}

1997 USAMO (Problems • Resources)
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