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MathGroup Archive 2006

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Re: solving an equation with sums

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67482] Re: solving an equation with sums
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 28 Jun 2006 03:51:22 -0400 (EDT)
  • References: <e7qmi0$6lb$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
Solve deals primarily with linear and polynomial equations. Your 
equation is a transcendental one. You will remember, that in C (complex) 
Exp[] is a periodic function. You will therefore get infinite many 
solutions. Try Reduce that is more powerful than Solve.
Daniel

newbix at bk.ru wrote:
> Hello,
> 
> I try to solve the following equation:
> sum[2*(1-e^(-x*t[[i]])-F[[i]])*t[[i]]*e^(-x*t[[i]]),{i,1,10}]==0
> where t and F are lists. Each list has ten entries.
> I tried to solve this sum using the following command:
> ------------------------------------------------------
> Solve[2*(1 - \[ExponentialE]^(-x*0.1) - 2810)*0.1*\[ExponentialE]^(-x*0.1) + 
>       2*(1 - \[ExponentialE]^(-x*0.2) - 5411)*0.2*\[ExponentialE]^(-x*0.2) + 
>       2*(1 - \[ExponentialE]^(-x*0.3) - 8701)*0.3*\[ExponentialE]^(-x*0.3) + 
>       2*(1 - \[ExponentialE]^(-x*0.4) - 13130)*0.4*\[ExponentialE]^(-x*0.4) + 
>       2*(1 - \[ExponentialE]^(-x*0.5) - 17327)*0.5*\[ExponentialE]^(-x*0.5) + 
>       2*(1 - \[ExponentialE]^(-x*0.6) - 24899)*0.6*\[ExponentialE]^(-x*0.6) + 
>       2*(1 - \[ExponentialE]^(-x*0.7) - 31230)*0.7*\[ExponentialE]^(-x*0.7) + 
>       2*(1 - \[ExponentialE]^(-x*0.7) - 40006)*0.8*\[ExponentialE]^(-x*0.8) + 
>       2*(1 - \[ExponentialE]^(-x*0.8) - 59880)*0.9*\[ExponentialE]^(-x*0.9) + 
>       2*(1 - \[ExponentialE]^(-x) - 80017)*\[ExponentialE]^(-x) == 0, x]
> -----------------------------------------
> but I got the following error message:
> 
> Solve::"tdep": "The equations appear to involve the variables to be solved \
> for in an essentially non-algebraic way."
> 
> What's wrong? How can I solve this expression using Mathematica?
> 
> Thank you in advance!
> 


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