       Re: Different (real) solutions using Solve for same

• To: mathgroup at smc.vnet.net
• Subject: [mg101841] Re: [mg101807] Different (real) solutions using Solve for same
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 19 Jul 2009 07:14:03 -0400 (EDT)

```You are missing a plus operator between two of the terms in your second equation

eqn1 = w/p == 25 e^2/(e + w)^2;

soln1 = Solve[eqn1, w] // FullSimplify;

eqn2 = p*(e + w)^2*# & /@ eqn1 // ExpandAll

e^2*w + 2*e*w^2 + w^3 == 25*e^2*p

soln2 = Solve[eqn2, w];

Thread[(w /. soln1) == (w /. soln2)] // FullSimplify

{True,True,True}

Bob Hanlon

---- kristoph <kristophs.post at web.de> 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?