Difference between revisions of "1997 USAMO Problems/Problem 5"
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[[File:USAMO97(5-solution).jpg]]== Problem == | [[File:USAMO97(5-solution).jpg]]== 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>. | ||
+ | |||
Prove that, for all positive real numbers <math>a, b, c,</math> | Prove that, for all positive real numbers <math>a, b, c,</math> | ||
Revision as of 09:20, 16 January 2013
== Problem ==
Prove that, for all positive real numbers
.
Prove that, for all positive real numbers
.
Solution
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See Also
1997 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |