C) Am I Solving this Hyperbolic Functions Homework Correctly?

orbsoner
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Homework Statement


Attached is the problem


Homework Equations



My question is am i going about it the right way for question C). I have done A and B and am sure they are correct.


The Attempt at a Solution


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orbsoner said:
[am i going about it the right way for question C).
I don't think so.
Look at how you solved b). What relationship between the coefficients did the method depend upon? E.g. suppose the constant term had been something other than -2. Would that have radically changed the method of solution? What about the other two?
When you've determined what the relationship is, you need to scale x to make the more general equation satisfy that relationship.
 
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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