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Re: Different (real) solutions using Solve for same equation

• To: mathgroup at smc.vnet.net
• Subject: [mg101847] Re: [mg101807] Different (real) solutions using Solve for same equation
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 19 Jul 2009 07:15:10 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200907180848.EAA06417@smc.vnet.net>
• Reply-to: murray at math.umass.edu

You have a typo in your second Solve, below.  Once you fix that, you 
should obtain the same solutions:

   old = Solve[w/p == 25 e^2/(e + w)^2, w];
   new = Solve[w^3 + 2 e w^2 + w e^2 == 25 p e^2, w];
   old == new
True

kristoph wrote:
> Dear all,
> 
> I came across the following observation which I find troublesome.
> 
> I was trying to solve the equation w/p == 25 e^2 / (e + w)^2 using
> Solve[w/p == 25 e^2 / (e + w)^2 , w]. But the non-complex solution did
> not have the properties I wanted.
> 
> I tested whether the solution was right and tried solving w^3 + 2 e
> w^2 w e^2 == 25 p e^2 (which is just rewriting the first equation)
> using Solve[w^3 + 2 e w^2 w e^2 == 25 p e^2, w].
> 
> This time the properties were present and the two non-complex
> solutions using the first and second approach where different. I would
> like to know why? Each equation can be transformed into the other via
> simple operations, why are there different solutions to it?
> 
> Thanks for answer.
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Different (real) solutions using Solve for same equation ?
    • From: kristoph <kristophs.post@web.de>