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Re: Resolve a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89717] Re: Resolve a function
  • From: Torsten Hennig <Torsten.Hennig at umsicht.fhg.de>
  • Date: Thu, 19 Jun 2008 05:40:35 -0400 (EDT)

>Dear all,
>I am new with mathematica. I would be grateful if >someone could tell
>me how can I find the general solutions of the r for the >following
>function f(r_) = 14.4* ((2/Sqrt[r^2 + R^2]) - 1/r ) >(where
>R=constant). I just want to express the function as r >=.....*f. Is
>this possible with mathematica.
>Thank you.

f = 14.4*(2/sqrt(r^2+R^2)-1/r)
-> f/14.4*r*sqrt(r^2+R^2)=2*r-sqrt(r^2+R^2)
-> (f/14.4*r+1)*sqrt(r^2+R^2)=2*r
-> (f/14.4*r+1)^2*(r^2+R^2)=4*r^2
-> ...
-> r^4+2/y*r^3+(R^2-3*(14.4/y)^2)*r^2+2/y*R^2*r+...
   ...+(14.4/y)^2*R^2 = 0

This is a quartic polynomial equation. 

Take a look at
http://reference.wolfram.com/mathematica/tutorial/NumericalSolutionOfPolynomialEquations.html
how to solve them analytically and numerically in
Mathematica.
Be careful: maybe not all solutions of the polynomial equation will be solutions of your original equation.

Best wishes
Torsten.


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