(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that if x^{2}= y^{2}then x=y or x = -y

2. Relevant equations

The 12 Properties of numbers

3. The attempt at a solution

I think I should do this case-wise:

Case (a) if x=y then x^{2}= x*x=y*y=y^{2}. Simple enough.

Case (b) if x = -y then x^{2}= x*x=(-y)*(-y) = ...

So what is left to show is that (-y)*(-y) = y*y which is where I am getting stuck.

I was thinking of doing something like:

(-y)(-y) = (-y)(-y)*1 = (-y)(-y) * [(-y)(-y)]*[(-y)(-y)]^{-1}

... but I don't see this going anywhere really. Any thoughts?

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# Spivak Calculus: Problem 1-(iii)

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