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.