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#1 2008-01-07 20:54:23

tony123
Member
Registered: 2007-08-03
Posts: 189

find the maximum

let

be distinct real numbers such that


and


find the maximum value of

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#2 2010-12-11 00:45:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: find the maximum

Hi tony123;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2011-04-03 16:18:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: find the maximum

Update to the above problem at the request of gAr to see my solution.

I was able to eliminate the numerical methods and come up with a quasi analytical method.

Using ac = bd

Using Lagrangian multipliers:

Adding the constraint ( 2 ) to the above equations:

Solving the simultaneous set of non linear equations:

Using b as a free parameter we can generate my original solution and all the rotations. Of course a is generated using ac = bd.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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