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Re: Are some equations unsolvable?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128067] Re: Are some equations unsolvable?
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Thu, 13 Sep 2012 03:38:24 -0400 (EDT)
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f = (1/(sigma*Sqrt[2 Pi]))*Sqrt[(Pi/(-1/(2*sigma^2)))]*
  Exp[((m/sigma^2)^2)/4*(-1/2*sigma^2) + (m^2/(2*sigma^2))]

(E^((3*m^2)/(8*sigma^2))*Sqrt[-sigma^2])/sigma

Solve[f == 216, {m, sigma}, VerifySolutions -> True]

Solve::ifun: Inverse functions are being used by Solve, so some
solutions may not be found; use Reduce for complete solution
information. >>

Solve::svars: Equations may not give solutions for all "solve" variables. >>

{}

There are no solutions. If sigma is a real number then Sqrt[-sigma^2}
is complex and f cannot equal 216.

Simplify[f, Element[sigma, Reals]]

(I*E^((3*m^2)/(8*sigma^2))*Abs[sigma])/sigma

Simplify[f, sigma > 0]

I*E^((3*m^2)/(8*sigma^2))


Bob Hanlon


On Wed, Sep 12, 2012 at 3:00 AM, Sergio Sergio <zerge69 at gmail.com> wrote:
> Hi,
> This is what I have:
>
> f = (1/(sigma*Sqrt[2 Pi]))*Sqrt[(Pi/(-1/(2*sigma^2)))]*
>   Exp[((m/sigma^2)^2)/4*(-1/2*sigma^2) + (m^2/(2*sigma^2))]
>
> Solve[f == 216, sigma]
>
> And I get this message: "This system cannot be solved with the methods available to Solve"
>
> Is it because there is no way to isolate sigma? Or am I doing something wrong?
>
> Thanks
>



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