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

(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 <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 ==
 

Revision as of 20:10, 1 July 2011