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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: 10,315
Registered: 7/15/05
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Oct 31, 2013 1:40 PM
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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
Read x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
David C. Ullrich
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/26/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Karl-Olav Nyberg
10/26/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/26/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Peter Percival
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
David C. Ullrich
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Don Coppersmith
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Don Coppersmith
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
gnasher729
10/25/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Peter Percival
10/27/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
gnasher729
10/27/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
dan.ms.chaos@gmail.com
10/27/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Peter Percival
10/27/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
fom
10/30/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/30/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Peter Percival
10/30/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/31/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
10/31/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
quasi
11/1/13
Read Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Phil Carmody

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