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## Homework Statement

By expanding (x-y)^2, prove that x^2 +y^2 ≥ 2xy for all real numbers x & y.

## Homework Equations

## The Attempt at a Solution

expanding (x-y)^2

x^2 - 2xy + y^2= 0

Hence, x^2 + y^2 = 2xy

But where does the ≥ come into it? and why?

when you put values in (except i which is not real of course) they all come out as = 2xy, which does satisfy ≥2xy, but why does this come into it??

Some insight would be fantastic!