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

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.