1) For any x > 0 and 0 ≤ h < 1 we have (x + h)^2 ≤ x^2 + h(2x + 1). 2) For any x > 0 and p > 0 with x^2 < p there exists y > x with y^2 < p. Prove the following statements (only using the axioms for the real numbers). At each step say which axiom you use. The problems is that my professor expects everyone to know how to do this from previous class; however my former professor never explained anything like this. I don't want an answer but I am hoping someone could guide me through proving this. So, could anyone help me get started, I really have no idea where to begin.