Let the first integer be x
Second integer be x + 2
Product of the two integers = 624
Equation:
(x) (x + 2) = 624
x² + 2x = 624
Transform to quadratic equation ax² + bx +c = 0
x² + 2x - 624 = 0
Solve by factoring or quadratic formula.
By factoring:
x² + 2x - 624 = 0
(x - 24) (x + 26) = 0
x - 24 = 0 x + 26 = 0
x = 24
Choose the positive root, x = 24.
First even integer: x ⇒ 24
Second integer: x + 2 = 24 + 2 ⇒ 26
The two consecutive even integers are 24 and 26.
Check:
(24) (26) = 624
624 = 624
