Since a and b are roots of y² + 5y - 11, we have
y² + 5y - 11 = (y - a) (y - b)
and expanding the right side gives
y² + 5y - 11 = y² - (a + b) y + ab
so that
a + b = -5
ab = -11
Now,
(a + 3) (b + 3) = ab + 3 (a + b) + 9
(a + 3) (b + 3) = -11 + 3 (-5) + 9
(a + 3) (b + 3) = -17
