Simply Typed Lambda Calculus question - Beta Reduction

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Homework Statement


Under the assumption that BETA is a closed term show that (λx.α)(β) and α[x→β] are logically equivalent.


Homework Equations


I'm sure I have to use β-reduction but I'm not sure how in this case:

⊢(λx.x)(β→α[x→β]



The Attempt at a Solution

 
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What does α[x→β] mean?
 

Thread 'Finding the nth roots of a complex number'

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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