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.