Senior Kangaroo 2022 Q10

The equations $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ both have real roots. It is known that the sum of the squares of the roots of the first equation is equal to the sum of the squares of the roots of the second one, and that $a e b$. Find the value of $500 + 10(a + b)$.