Question

The product of two consecutive positive integers is 306. Find the integers.

Answer 1

Let two consecutive positive integers be x and x + 1.

According to the question,

Product of x and (x + 1) = 306

i.e., x(x + 1) = 306

⇒ x² + x – 306 = 0

⇒ x² + 18x – 17x – 306 = 0

⇒ x(x + 18) – 17(x + 18) = 0

⇒ (x + 18)(x – 17) = 0

⇒ x = 17 and –18   ...[Neglecting –18]

Hence, numbers are x = 17 and (x + 1) = 18.