Question

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

Answer 1

Let the first integer = x
then second integer = x + 1
and third integer = x + 2
Now according to the condition,
x² + (x + 1)(x + 2) = 154
⇒ x² + x² + 3x + 2 - 154 = 0
⇒ 2x² + 3x - 152 = 0
⇒ 2x² + 19x - 16x - 152 = 0
⇒ x(2x + 19) - 8(2x + 19) = 0
⇒ (2x + 19)(x - 8) = 0
Either 2x + 19 = 0,
then 2x = -19

⇒ x = `-(19)/(2)`
But it is not possible as it is not an positive integer.
or
x - 8 = 0,
then x = 8
∴ Numbers are 8, (8 + 1) - 9 and (8 + 2) = 10.