There are three consecutive positive integers such that the sum of thesquare of the first and the product of the other two is 154. What are theintegers?.

Let the three consecutive positive integers be x, x + 1 and x + 2.
x ² + (x + 1)(x + 2) = 154
x ² + x ² + 3x + 2 = 154
2x ² + 3x - 152 = 0
2x ² + 19x – 16x – 152 = 0
x(2x + 19) – 8(2x + 19) = 0
(x – 8)(2x + 19) = 0
x = 8 or

∴ The integers are 8, 9 and 10.
Checking:
8 ² + 9 × 10 = 64 + 90 = 154.