Find three positive consecutive integers such that the product of the smallest and the largest is 17 more than three times the median integer

There are two answers to this question

the first possible answer is 5, 6, and 7 and the second possible answer is - 4, - 3, and - 2

Step-by-step explanation:

let the three numbers be (x-1), x, and (x+1)

the product of the smallest and largest number is 17 more than 3 times the middle number, or

(x-1) (x+1) = 3x+17, or

x^2-1 = 3+17, or

x^2-3x-18 = 0

(x-6) (x+3) = 0

So x = 6 or - 3

Then just subtract one and add one to get the other integers. the three numbers are 5, 6, and 7 or - 4, - 3, and - 2