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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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: find the maximum

Hi tony123;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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