Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Replies: 20   Last Post: Nov 1, 2013 4:48 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Phil Carmody

Posts: 2,205
Registered: 12/7/04
Re: x + y + z >= xyz implies x^2 + y^2 + z^2 >= Axyz
Posted: Nov 1, 2013 4:48 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

quasi <quasi@null.set> writes:
> 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
> >
> >My solution is elementary (avoids Calculus), but if a method
> >based on Calculus yields an easy resolution, that would be worth
> >seeing as well.

>
> As a number of people have surmised, the maximum possible
> value of A is sqrt(3).
>
> Here's a proof ...

...
> contradiction, which completes the proof.

That is a lovely mathematical puzzle, thanks for posting it!

Phil
--
The list of trusted root authorities in your browser included the
United Arab Emirates-based Etisalat, which was caught secretly
uploading spyware onto 100,000 customers' BlackBerries.
http://www.wired.com/threatlevel/2009/07/blackberry-spies/



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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.