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

1.	The product of two consecutive positive integers is 306. Find the integers.
Answer» Let the two consecutive positive integers be x and (x + 1) According to the given condition, 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 + 18 = 0 or x - 17 = 0 ⇒ x = - 18 or x = 17 ∴ x = 17 (x is a positive integers) When x = 17, x + 1 = 17 + 1 = 18 Hence, the required integers are 17 and 18.

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

Answer»

Let the two consecutive positive integers be x and (x + 1)

According to the given condition,

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 + 18 = 0 or x - 17 = 0

⇒ x = - 18 or x = 17

∴ x = 17 (x is a positive integers)

When x = 17,

x + 1 = 17 + 1 = 18

Hence, the required integers are 17 and 18.