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

Revision as of 09:20, 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 $a, b, c,$

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

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@@ Line 1: / Line 1: @@
 [[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>

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