1. ## Statement Proof

Prove that iff a and b are real numbers, then a^2+b^2 (>=) 2ab

2. $\displaystyle a^2 + b^2 \geq 2ab$ iff $\displaystyle a^2 - 2ab + b^2 \geq 0$ iff $\displaystyle (a-b)^2 \geq 0$.

3. thanks a lot for that. is there any way i can condition my mind to pick up proofs and be able to do them much easier because im having a lot of trouble trying to do proofs right now. just recently started doing similar sorts of proofs in uni and i find myself finding it very hard to do it independently and when i get given the solutions, i understand it completely and i know i am completely capable of solving them but i just cant see the correct path most times

for example this question: The sum of 2 rational numbers is rational.

and here is my solution: a/b + c/d = ad/bd +cb/bd = (ad+cb)/bd
i always find something resembling a proof but i have constantly feel that something is missing. for this situation do i have to state that a,b,c,d are also rational numbers and assuming the multiplication of rational numbers also results in a rational number because i constantly get the feeling that i also have to prove my assumption or the solution doesnt feel complete.