Finding the subnormal using Descartes normal method

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Homework Statement



find the subnormal using Descartes normal method.

Homework Equations



f\left( x \right)\; =\; \frac{1}{x},\;

The Attempt at a Solution



i get an 4th degree equation in x!

however this is my first post and i really wanted to try the LateX thing. first time.

Homework Statement


Homework Equations


The Attempt at a Solution

 
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obviously i suck at LateX
 


Is the function f(x) = 1/x?

How is the subnormal defined? I've never heard of it, or the Descartes normal method, either. Possibly you are using different terminology.
 
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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