Closed Form solution too much to hope for?

*To*: mathgroup at smc.vnet.net*Subject*: [mg66721] Closed Form solution too much to hope for?*From*: "DOD" <dcodea at gmail.com>*Date*: Sat, 27 May 2006 21:03:35 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I don't have a very good idea on the guts of Solve, or what its reasonable to expect from mathematica, but here's what I want: T is the solution to d x^n + (1-d) x^2 == c Where n, d and c are parameters of my model. Now, it's very clear what this solution looks like; as we vary d the solution 'slides' from the easy-to-solve-in-a-closed-form solutions to x^n=c and x^2=c, that is, x=c^{1/2} and x=c^{1/n}. So I know what the solution looks like, but when I leave it in symbolic form, Solve doesn't like it, and says it's fundamentally not algebraic. I presume this is because the number of roots depends on n, which isn't given, so Solve panics. But I only really care about the real solution between 0 and 1- is there any way to get the form of this solution as a function of both n and c? Thanks for enlighening me. Dennis

**Follow-Ups**:**Re: Closed Form solution too much to hope for?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>