Please derive equation 2.27 in Goldstein(3rd ed.)

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Please derive equation 2.27 in Goldstein(3rd ed.)
 
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merrypark3 said:
Please derive equation 2.27 in Goldstein(3rd ed.)

And how do we know what we're supposed to derive if you haven't given us anything except a location no one will find. You should at least try to derive the equation first.
 
and please at lest post the equation...
 
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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