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