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MathGroup Archive 2006

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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


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