Prove that every pair of integers whose sum of squares is even also has an even sum Consider the quadratic equation x 2 + bx + c = 0, where b, c ∈ Q. Suppose that this equation has two distinct real r

Prove that every pair of integers whose sum of squares is even also has an even sum

Consider the quadratic equation x 2 + bx + c = 0, where b, c ∈ Q. Suppose that this equation has two distinct real roots, x1 and x2. Prove that, if one of those roots is rational, then so is the other.