Question

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

Answer 1

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


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