Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]
 quasi Posts: 12,067 Registered: 7/15/05
x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Oct 25, 2013 7:23 AM

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

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