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## Homework Statement

Prove for all real numbers x and y that [tex]2xy =< x^2 + y^2[/tex]

## Homework Equations

## The Attempt at a Solution

Well, since this is a problem regarding proof, I thought I would start with a contradictory statement like:

2xy >= x^2+y^2

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

0 >= (x-y)^2

Since (x-y)^2 is either a positive integer and a zero,

0 =< (x-y)^2

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

2xy =< x^2+y^2

Well that's all I can think of... can anyone point out any mistakes or anything? Is there more to it than just this?