Date: Oct 25, 2013 7:23 AM
Author: quasi
Subject: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz

Here's a nice challenge problem which I adapted from a past
competition problem ...

Problem:

Find, with proof, the largest real number A such that

x + y + z >= xyz

implies

x^2 + y^2 + z^2 >= Axyz

My solution is elementary (avoids Calculus), but if a method
based on Calculus yields an easy resolution, that would be worth
seeing as well.

quasi