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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 25, 2013 1:54 PM

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

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