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Re: from Rumen, MEXICO, petition

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  Re: from Rumen, MEXICO, petition Robert Rosenbaum <robertr@math.uh.edu> - 2011-04-11 11:07 +0000

#1596 — Re: from Rumen, MEXICO, petition

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@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.
>
>

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