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Different (real) solutions using Solve for same equation ?

• To: mathgroup at smc.vnet.net
• Subject: [mg101807] Different (real) solutions using Solve for same equation ?
• From: kristoph <kristophs.post at web.de>
• Date: Sat, 18 Jul 2009 04:48:16 -0400 (EDT)

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.

• Follow-Ups:
  • Re: Different (real) solutions using Solve for same equation
    • From: Murray Eisenberg <murray@math.umass.edu>