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
Deadline expired on October 12, 2009.
Solution. By the Cauchy-Schwarz inequality,
Applying the AM-GM inequality
we can establish
5 students sent a solution. 5 points: Backhausz Tibor, Frankl Nóra, Nagy 235 János, Nagy 648 Donát. 0 point: 1 student.