Question

The product of two consecutive positive integers is 156. Find the integers.

Answer 1

Given:

Let the smaller integer be x.

Then the next consecutive integer is x + 1.

x(x+1) = 156

x² + x = 156

⇒ x² + x − 156 = 0

We need two numbers that multiply to −156 and add to +1.

Try factor pairs of 156:

13 × 12 = 156, and 13 − 12 = 1

x² + x − 156

= (x + 13) (x − 12) = 0

Solve for x

x + 13 = 0 or x − 12 = 0

x = −13 or x = 12

Since we want positive integers, we take:

x = 12, x + 1 = 13

12 and 13​