Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Replies: 20   Last Post: Nov 1, 2013 4:48 AM

 Messages: [ Previous | Next ]
 Peter Percival Posts: 1,623 Registered: 10/25/10
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Oct 25, 2013 8:41 PM

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

A = sqrt 3.

> 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
>

--
The world will little note, nor long remember what we say here
Lincoln at Gettysburg

Date Subject Author
10/25/13 quasi
10/25/13 David C. Ullrich
10/25/13 quasi
10/26/13 Karl-Olav Nyberg
10/26/13 quasi
10/26/13 Peter Percival
10/25/13 David C. Ullrich
10/25/13 Don Coppersmith
10/25/13 Don Coppersmith
10/25/13 gnasher729
10/25/13 Peter Percival
10/27/13 gnasher729
10/27/13 dan.ms.chaos@gmail.com
10/27/13 Peter Percival
10/27/13 fom
10/30/13 quasi
10/30/13 Peter Percival
10/30/13 quasi
10/31/13 quasi
10/31/13 quasi
11/1/13 Phil Carmody