Suppose that you have three consecutive positive integers where the product of the smaller and larger number is equal to 15 more than 6 times the middle number. find the 3 numbers, be sure to include all possibilities.

The numbers are either {-3, -2, -1} or {7, 8, 9}.

Step-by-step explanation:

Let the smallest integer be represented by x. The middle number is x+1, and the largest number is x+2.

The product of the smaller and larger number is (x)(x+2).

15 more than 6 times the middle number is 6(x+1)+15.

(x)(x+2)=6(x+1)+15

x^2+2x=6x+6+15

x^2+2x=6x+21

x^2-4x-21=0

(x-7)(x+3)=0

x=-3 or x=7

The numbers are either {-3, -2, -1} or {7, 8, 9}.