Re: from Rumen, MEXICO, petition
- To: mathgroup at smc.vnet.net
- Subject: [mg118073] Re: from Rumen, MEXICO, petition
- From: Robert Rosenbaum <robertr at math.uh.edu>
- Date: Mon, 11 Apr 2011 07:07:52 -0400 (EDT)
While I agree that there is clearly no real solution, there may be a complex solution. Indeed, eliminating one of the terms yields several: In[14]:= Length[Solve[11*Exp[-Es/135] + 10.5*Exp[-Es/425] + 2.02912 == 0]] Out[14]= 85 I don't know how to solve the full equation, but I'd guess that equations of that form are generally impossible to solve analytically and difficult to solve numerically. I didn't have the patience to wait longer, but FindInstance failed to find a solution within a minute or so on my machine. Best, Robert On Apr 9, 2011, at 4:59 PM, Bill Rowe wrote: > On 4/9/11 at 7:11 AM, rumen5252 at yahoo.com.mx (Rumen Ivanov) wrote: > >> 11*Exp[-Es/135]+10.5*Exp[-Es/425]+ 4.899*Exp[-Es/1754]+ 2.02912 = 0 >> Please tell me how Mathematica can solve this equation for Es? With >> the derivatives of "Solve" it is impossible. > > There is no solution. Each of the terms in your expression has > the form a*Exp[-Es/b] with a and b being positive reals. So, > each term is a positive real for all real values of Es. Your > expression has a global minimum value of 2.02912 at Es = > +Infinity and increases to +Infinity as Es tends to -Infinity. > >