
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted:
Nov 1, 2013 4:48 AM


quasi <quasi@null.set> writes: > quasi 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 > > > >My solution is elementary (avoids Calculus), but if a method > >based on Calculus yields an easy resolution, that would be worth > >seeing as well. > > As a number of people have surmised, the maximum possible > value of A is sqrt(3). > > Here's a proof ... ... > contradiction, which completes the proof.
That is a lovely mathematical puzzle, thanks for posting it!
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