       Re: Are some equations unsolvable?

• To: mathgroup at smc.vnet.net
• Subject: [mg128070] Re: Are some equations unsolvable?
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Thu, 13 Sep 2012 03:39:24 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• References: <k2pc54\$99t\$1@smc.vnet.net>

```On 12 Sep., 09:05, Sergio Sergio <zerg... 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

As a first step try to tell Mathematica something about sigma, for
instance that sigma >0:

In:= fs = Simplify[f, sigma > 0]

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

Then Mathematica can solve your equation easily:

In:= Solve[216 == fs, sigma]

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

Out= {
{sigma -> -(((-1)^(1/4)*m)/(2*Sqrt[(1/3)*(Pi + 2*I*Log)]))},
{sigma -> ((-1)^(1/4)*m)/(2*Sqrt[(1/3)*(Pi + 2*I*Log)])}}

By the way your expression looks very similar to a normal distribution
but with strange signs. Are you sure that this is the expression you