Find three positive consecutive integers such that the product of the smallest and the largest is 17 more than three times the median integer.
+23254 Since they are consecutive integers, they can be labeled: a, a + 1, and a + 2
Product of the smallest and largest: a(a + 2)
17 more than three times the median integer: 17 + 3(a + 1)
The equation: a(a + 2) = 17 + 3(a + 1)
a2 + 2a = 17 + 3a + 3
a2 - a - 20 = 0
(a - 5)(a + 4) = 0
Either a = 5 or a = -4
Since they must be positive, we can only use a = 5 ---> a + 1 = 6 ---> a + 2 = 7
