Find two consecutive positive even integers whose product is 224.

Let two consecutive even numbers be x and x + 2.

Given,

Product of numbers is 224.

⇒ x(x + 2) = 224

⇒ x² + 2x - 224 = 0

⇒ x² + 16x - 14x - 224 = 0

⇒ x(x + 16) - 14(x + 16) = 0

⇒ (x - 14)(x + 16) = 0

⇒ (x - 14) = 0 or (x + 16) = 0     [Using zero -product rule]

⇒ x = -16 or x = 14

Since we need positive even integers, x = 14

⇒ x + 2 = 14 + 2 = 16.

Hence, two consecutive positive even integers are 14 and 16.