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

(x + 9) = 0 or (x - 8) = 0

 x = -9 or x = 8

∴ Value of x = 8 [since, -9 is not positive]

∴ First even integer = 2x 

= 2 × 8

= 16

and second even integer

= 16 + 2

= 18