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

• To: mathgroup at smc.vnet.net
• Subject: [mg101851] Re: Different (real) solutions using Solve for same equation ?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sun, 19 Jul 2009 07:15:54 -0400 (EDT)

```On 7/18/09 at 4:48 AM, kristophs.post at web.de (kristoph) wrote:

>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?

The way the first problem was written, neither p = 0 nor e+w = 0
are allowed since these values cause one side or the other of
the equation to be infinite. When you re-write the equation to
eliminate the division, this restriction no longer exists.

That is the re-write you did implicitly assumes certain values
are not zero. Mathematica never makes such assumptions.

```

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