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?
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