Math Help, solution step by step

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solution step by step
 

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Can you describe the iteration method?
 
Use the Newton-raphson method or you can use your own iterative method...but doing it the latter way may fail to converge to a rootN-R form: \alpha_{n+1}=\alpha_n -\frac{f(\alpha_n)}{f'(\alpha_n)}
 
Buit the crucial point is YOUR method. Whatever method you use, YOU are supposed to do it. Have you tried using Newton-Raphson?

This is, I think, now the fourth problem you have posted with no sign of attempting it yourself.
 
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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