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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

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 quasi Posts: 12,067 Registered: 7/15/05
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Oct 31, 2013 1:40 PM

quasi wrote:
>
>Here's a variation ...
>
>For x,y,z > 0, find the largest real number A such that
>
> x - y - z >= xyz
>
>implies
>
> x^2 + y^2 + z^2 >= Axyz
>
>Calculus allowed, as well as a CAS, if needed.
>
>Required is an algebraically exact answer for A.
>
>Just an answer will suffice -- no proof required.

Change that to:

Proof required, but the proof can be CAS-assisted.

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