1. The problem statement, all variables and given/known data Prove for all real numbers x and y that [tex]2xy =< x^2 + y^2[/tex] 2. Relevant equations 3. 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?