On Fri, 25 Oct 2013 07:20:29 -0500, quasi <firstname.lastname@example.org> wrote:
>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
I'm assuming you meant to restrict to x, y, z >= 0. The largest such A is 0.
If x = y = 1 then
>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