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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: [mg50321] Re: [mg50300] Q: Solve gives complex solution where there is a noncomplex solution how to get the last one?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 27 Aug 2004 02:57:34 -0400 (EDT)
• References: <200408261050.GAA16310@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 26 Aug 2004, at 19:50, Dick Barends wrote:

> *This message was transferred with a trial version of CommuniGate(tm) 
> Pro*
> 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
>
>
>
Use

Solve[x y / ( 1 + y^2 )^(1/2) == a, y]

In Mathematica 0.5 and 1/2 are quite different entities and you should 
not use them interchangeably. If you really mean the square root you 
should always use the power 1/2.

Andrzej Kozlowski

• References:
  • Q: Solve gives complex solution where there is a noncomplex solution how to get the last one?
    • From: "Dick Barends" <dick.barends@wxs.nl>