Question

If the product of two consecutive even integers is 224, find the integers.

Answer 1

Let first even integer = 2x

then second even integer = 2x + 2

According to the condition,

2x × (2x + 2) = 224

⇒ 4x² + 4x - 224 = 0

⇒ x² + x - 56 = 0

⇒ x² + 8x - 7x - 56 = 0

⇒ x(x + 8) -7(x + 8) = 0

⇒ (x + 8)(x - 7) = 0

Either x + 8 = 0,

then x = -8

∴ First even integer = 2 × (-8) = -16

and second even integer = -16 + 2 = -14

or

x - 7 = 0,

then x = 7

∴ First even integer = 2x = 2 × 7 = 14

and second even integer = 14 + 2 = 16.