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Re: Are some equations unsolvable?

On 12 Sep., 09:05, Sergio Sergio <zerg... at> 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[37]:= fs = Simplify[f, sigma > 0]

Out[37]= I*E^((3*m^2)/(8*sigma^2))

Then Mathematica can solve your equation easily:

In[38]:= Solve[216 == fs, sigma]

During evaluation of In[38]:= Solve::ifun:Inverse functions are being
used by Solve, so some solutions may not be found; use Reduce for
complete solution information. >>

Out[38]= {
   {sigma -> -(((-1)^(1/4)*m)/(2*Sqrt[(1/3)*(Pi + 2*I*Log[216])]))},
   {sigma -> ((-1)^(1/4)*m)/(2*Sqrt[(1/3)*(Pi + 2*I*Log[216])])}}

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
had in mind?


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