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MathGroup Archive 2004

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Re: Q: Solve gives complex solution where there is a noncomplex solution how to get the last one?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50322] Re: [mg50300] Q: Solve gives complex solution where there is a noncomplex solution how to get the last one?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 27 Aug 2004 02:57:44 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200408261050.GAA16310@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

You used approximate (machine) numbers in the equation, namely, the 
exponent, so you got machine numbers in your answer.

But:

  Solve[x y/Sqrt[1 + y^2] == a, y] // InputForm

{{y -> -(a/Sqrt[-a^2 + x^2])},
  {y -> a/Sqrt[-a^2 + x^2]}}

(I'm using InputForm on the result of Solve just to obtain the answer in 
a linear form suitable for e-mail rather than Mathematica's default 2D 
StandardForm.)

Dick Barends wrote:

> Hello,
> 
> The following line
> 
> Solve[x y / ( 1 + y^2 )^0.5 == a, y]
> 
> Gives a complex solution : (0.+ i )a / (a^2 - x^2)^0.5
> Which is correct but could be simpler, not complex
> 
> The solution I expected is: a/(x^2 - a^2)^0.5
> 
> How can I instruct Mathematica (Solve) to give the simple solution directly.
> 
> kind regards
> Dick Barends
> 
> 
> 

-- 
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


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