Question

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

Answer 1

Answer:

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