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Re: unwanted Complex result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91598] Re: unwanted Complex result
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 28 Aug 2008 07:39:49 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g95k8a$543$1@smc.vnet.net>

John Rivers wrote:

> Solve[
> (Sqrt[speed ^ 2 - windx ^ 2] + windy) / a speed ^ 2 + b speed + c ==
> distance / height
> , speed]
> 
> this works but returns 4 solutions that all return complex numbers
> 
> I need a real number

You could use either *Reduce[eqns, vars, Reals]* with a domain 
specification (third argument) or *Cases[]* as in the following:


   With[{windx = 10, windy = 2, a = 3, b = 5, c = 7, distance = 100,
     height = 40},
    Module[{eqn = (Sqrt[speed^2 - windx^2] + windy)/a speed^2 + b speed +
          c == distance/height},
     Print[N[Solve[eqn, speed]]];
     Print[N[Reduce[eqn, speed, Reals]]];
     Print[N[
       Cases[Solve[eqn, speed],
        s_ /; (Chop[Im[speed /. s]] == 0) -> s]]]]]

   {{speed->-0.678225-0.300835 I},{speed->-0.678225+0.300835 I},
    {speed->0.385283-1.72241 I},{speed->0.385283+1.72241 I}}

   False

   {}

Regards,
-- Jean-Marc


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