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

Revision as of 11:02, 17 September 2012

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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 {{USAMO newbox|year=1997|num-b=4|num-a=6}}
+[[Category:Olympiad Algebra Problems]]
 [[Category:Olympiad Inequality Problems]]

1997 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions