Question

If the product of two positive consecutive even integers is 288, find the integers.

Answer 1

Let first positive even integer = 2x
then second even integer = 2x + 2
According to the condition,
2x × (2x + 2) = 288
⇒ 4x² + 4x – 288 = 0
⇒ x² + x – 72 = 0  ...(Dividing by 4)
⇒ x² - 9x - 8x - 72 = 0
⇒ x(x + 9) -8(x + 9) = 0
⇒ (x + 9)(x - 8) = 0
EIther x + 9 = 0,
then x = -9
But it is not possible as it is negative
or
x - 8 = 0,
then x = 8
∴ First even integer = 2x 
= 2 x 8
= 16
and second even integer
= 16 + 2
= 18.