Derivation of the equilibrium saturation ratio equation?

DM1984
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Homework Statement



S=1+(a/r)-(b/r^3)

Homework Equations



need to find r=sqrt(3b/a) and S=1+ sqrt((4a^3)/(27b))) from a derivation of the above formula in #1.

The Attempt at a Solution



0=(3b/r^4) - (a/r^2)
 
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DM1984 said:

Homework Statement



S=1+(a/r)-(b/r^3)

Homework Equations



need to find r=sqrt(3b/a) and S=1+ sqrt((4a^3)/(27b))) from a derivation of the above formula in #1.

The Attempt at a Solution



0=(3b/r^4) - (a/r^2)

So, what is preventing you from solving this equation?

RGV
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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