Question

(b) If a and b are rational numbers, then a^2 + b^2 > 2ab.

Answer 1

See explanation below.

Explanation:

We know that all squares are positive. Even the square of a negative number is positive ((-2)²= 4).

Therefore, we can say that (a-b)²≥0

⇒a²-2ab+b² ≥ 0

⇒a² + b² ≥ 2ab

Please notice that I added the possibility that (a-b)² "equals zero" and not only "it's greater than zero" because we don't know if a ≠ b. Since the problem doesn't state anything about this fact, there's the possibility that a = b, and then we would have that a - b = 0 and therefore (a - b)² = 0.