Does a Scalene Triangle Exist? Proving Its Existence with a Simple Construction

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Homework Statement



Prove that a scalene triangle exists

Homework Equations





The Attempt at a Solution



I really don't know how to approach this proof... should I do a direct proof or maybe by contradiction? Any help would be great...
 
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The easiest way to show something exists is to demonstrate one. So pick three points in the xy plane that give vertices of a scalene triangle and then verify it is.
 

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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