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

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== Solution ==
 
== Solution ==
{{solution}}
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{{[[File:solution]]}}
  
 
==See Also ==
 
==See Also ==

Revision as of 08:24, 16 January 2013

Problem

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

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

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

{{File:Solution}}

See Also

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