Optimization problem: Folding a triangle to minimize one side

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Homework Statement



The upper right-hand corner of a piece of paper, 12 in by 8 in is folded over to the bottom edge. How would you fold it to minimize the length of the fold? In other words, how would you choose x to minimize y?

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Homework Equations



None so far.

The Attempt at a Solution



I haven't a clue how to get started. I know I need to relate the length of y to the length of x and then differentiate and find the minima, but I don't know how to form the initial relationship.
 
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Hint -- use the 8x12" information as part of the equations your write. If x is as shown, then the bottom piece is 8-x, right? What can you say about the angles in the two triangles that are formed by that fold?
 

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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