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MathGroup Archive 2001

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Re: Solve[] for equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31936] Re: [mg31928] Solve[] for equations?
  • From: BobHanlon at aol.com
  • Date: Thu, 13 Dec 2001 01:08:40 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 12/12/01 5:51:22 AM, djvango at sandia.gov writes:

>I have a system of equations
>
>eq1 = Rac == R1(R2+R3+R4)/(R1+R2+R3+R4)
>eq2 = Rad == R2(R1+R3+R4)/(R1+R2+R3+R4)
>eq3 = Rbc == R3(R1+R2+R4)/(R1+R2+R3+R4)
>eq4 = Rbd == R4(R1+R2+R3)/(R1+R2+R3+R4)
>
>I'd like to get R1, R2, R3, and R4 in terms of Rac, Rad, Rbc, and Rbd.
> Four
>equations, four unknowns -- it seems simple in concept so I figured 
Mathematica
>could do it easily.  I thought that something along the lines of:
>
>Solve[{eqs},{R1, R2, R3, R4}] or
>Solve[{eqs}, R1, {R2, R3, R4}]
>
>would have worked, but these give {}.  They only permutation of commands
>that seemed to do anything was something like
>
>Solve[eq1, R1]
>
>but one can do that easily by hand so what's the point.
>
>Is there some other command I should be using besides Solve?   Is there
>some
>mathematical reason that I don't recognize as to why this won't work? 
> I
>would appreciate any insights.
>

You did not define eqs.  Solving a simplified version of your system:

eqs={Rac==R1(R2+R3)/(R1+R2+R3),Rad==R2(R1+R3)/(R1+R2+R3),
      Rbc==R3(R1+R2)/(R1+R2+R3)};

Solve[eqs, {R1, R2, R3}] // Simplify

{{R1 -> (Rac^2 + (Rad - Rbc)^2 - 
      2*Rac*(Rad + Rbc))/(2*(Rac - Rad - Rbc)), 
   R2 -> -((Rac^2 + (Rad - Rbc)^2 - 
       2*Rac*(Rad + Rbc))/
      (2*(Rac - Rad + Rbc))), 
   R3 -> -((Rac^2 + (Rad - Rbc)^2 - 
       2*Rac*(Rad + Rbc))/
      (2*(Rac + Rad - Rbc)))}}


Bob Hanlon
Chantilly, VA  USA


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