a and b are integers Prove that: 2ab <= a2 + b2 I have tested various values for a and b and determined that the statement seems to be generally true. I'm having a hard time though constructing a formal proof. It will not do to suppose the statement is wrong and then provide a counterexample. This would only prove that the statement is true for those particular values of a and b, and not for all values. I learned about mathematical induction but I think that method is used to prove statements about a well-ordered set. a and b can be any integer so I don't think that would work. I wondered what kind of statement may have simplified to produce a2 + b2 so I played with (a+b) * (a+b) which produced a2 + b2 + 2ab and also with (a-b) * (a-b) which produced a2 + b2 - 2ab. This looks similar to the original statement, and I feel like I may be onto some clues. Without giving me the answer, I wonder if someone could give me a push in the right direction?