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R1= Ra*Rb/(Ra + Rb +Rc)

R2= Ra*Rc/(Ra + Rb + Rc)

R3= Rb*Rc/(Ra + Rb + Rc)

This proof is fairly simple because through the parallel resistance formula

R1 + R3 = Rb(Ra+Rc)/(Ra+Rb+Rc)

R2 + R3 = Rc(Ra+Rb)/(Ra + Rb+Rc)

R2 + R1 = Ra(Rb+Rc)/(Ra + Rb +Rc)

you can do a back substitution of variables to solve for R1, R2, and R3.

No problem.

However, going the other way, that is----trying to solve for Ra, Rb, and Rc is not so simple, and leads to really messy polynomials.

I read somewhere that this is a topology problem and it is hard to solve using simple algebraic equations.

Can anyone enlighten me on why this is so? Or maybe I am mistaken, and there is a simple proof?

Thanks,

Nick