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Topic: Terrible algebraic system
Replies: 18   Last Post: Mar 8, 2012 4:26 AM

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 Robert Lewis Posts: 52 Registered: 7/17/08
Re: Terrible algebraic system
Posted: Feb 23, 2012 2:53 PM
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On Feb 22, 9:10 am, deltaquat...@gmail.com wrote:
> Hi,
>
> couldn't solve this with Wolfram Alpha, Matlab or Maxima:
>
> (a-L)^2/a*2/(a+b)-p=0
> (b-U)^2/b*2/(a+b)-p=0
>
> with a>L>0, b>U>0. Any tips? Should I resort to numerical methods?
>
> Best Regards
>
> Sergio Rossi

This is very easy to solve with the Dixon resultant, eliminating b.
(It's a very small system, so I'm sure lots of elimination techniques
would work.)

The resultant for a is:

2*pp^2*aa^4-6*pp*aa^4+4*aa^4-2*ll*pp^2*aa^3+2*uu*pp^2*aa^3+16*ll*pp*aa^3-4*uu*pp*aa^3-16*ll*aa^3+ll^2*pp^2*aa^2+uu^2*pp^2*aa^2
-16*ll^2*pp*aa^2+8*uu*ll*pp*aa^2+24*ll^2*aa^2+8*ll^3*pp*aa-4*uu*ll^2*pp*aa-16*ll^3*aa-2*ll^4*pp
+4*ll^4

If you'd like, I could easily find the resultant for b.

Robert H. Lewis
Fordham University

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