The product of two consecutive integers is 11 more than their sum. Find the integers

Step-by-step explanation:

Let the two consecutive integers be x, x + 1

Product of the two consecutive integers = x * (x+1) = x*x + x*1

= x² + x

sum of two consecutive integers = x + x + 1 = 2x + 1

x² + x - (2x + 1) = 11

x² + x - 2x - 1 = 11

x² - x - 1 - 11 = 0

x² - x - 12 = 0

x² - 4x + 3x - 12 = 0

x (x-4) + 3 (x-4) = 0

(x-4) (x + 3) = 0

x - 4 = 0 or x + 3 = 0

x = 4 0r x = - 3

If x = 4, the the consecutive numbers are 4 and 5

If x = - 3, the consecutive numbers are - 3 and - 2