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

let

be distinct real numbers such thatand

find the maximum value of

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

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

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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