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

Revision as of 16:09, 12 April 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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Revision as of 16:09, 12 April 2012 (view source) 1=2 (talk \| contribs) (added solution tag, USAMO box, and category) ← Older edit		Revision as of 16:09, 12 April 2012 (view source) 1=2 (talk \| contribs) m Newer edit →
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	{{USAMO box\|year=1997\|num-b=4\|after=Last Problem}}		{{USAMO box\|year=1997\|num-b=4\|after=Last Problem}}

−	[[Category:Olympiad ~~Inequailty~~ Problems]]	+	[[Category:Olympiad Algebra Problems]]

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