There are three consecutive integers such that the square of the first increased by the product of the other two gives 154. What are the integers?

Question

Philoid · Accepted Answer

Let the three consecutive numbers be a, a + 1, a + 2

Given, there are three consecutive integers such that the square of the first increased by the product of the other two gives 154.

⇒ a² + (a + 1)(a + 2) = 154

⇒ 2a² + 3a + 2 = 154

⇒ 2a² + 3a – 152 = 0

⇒ 2a² + 19a – 16a – 152 = 0

⇒ a(2a + 19) – 8(2a + 19) = 0

⇒ (a – 8)(2a + 19) = 0

Thus, a = 8

Numbers are 8, 9, 10