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[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? Regards, Wolfgang