Question

The product of two consecutive odd integers is 255. Find the integers.

Note: Each set of brackets represents one solution


100points

Answer 1

• (15, 17) and (- 17, - 15)

Explanation:

Let numbers be x and x + 2.

Their product is 255:

• x(x + 2) = 255
• x² + 2x = 255
• x² + 2x + 1 = 256
• (x + 1)² = 16²
• x + 1 = ± 16

• 1) x + 1 = 16 ⇒ x = 15 and x + 2 = 17
• 2) x + 1 = - 16 ⇒ x = - 17 and x + 2 = - 15