Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2008-01-08 19:54:23

tony123
Full Member

Offline

find the maximum

let

be distinct real numbers such that




and

find the maximum value of

 

#2 2010-12-11 23:45:32

bobbym
Administrator

Online

Re: find the maximum

Hi tony123;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#3 2011-04-04 14:18:55

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

Board footer

Powered by FluxBB