Problem A. 487. (September 2009)
A. 487. Let x, y, z be positive numbers satisfying xyz1. Prove that .
Proposed by Tuan Le, Anaheim, California, USA
(5 pont)
Deadline expired on 12 October 2009.
Solution. By the CauchySchwarz inequality,
Therefore
and similarly
and
Applying the AMGM inequality
and
we can establish
Statistics:
