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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 ]
 Karl-Olav Nyberg Posts: 1,575 Registered: 12/6/04
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Oct 26, 2013 1:55 PM

On Friday, October 25, 2013 7:50:36 PM UTC+2, quasi wrote:
> dullrich wrote:
>

> >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
>
> >
>
> >I'm assuming you meant to restrict to x, y, z >= 0.
>
>
>
> No -- x,y,z are only required to be real.
>
>
>
> quasi

If x, y and z can be any real number then A can be any number. If x, y and z all equals 0 then A can be whatever it wants :) So there must be som conditions to the problem.

KON

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