There are three consecutive odd integers where the product of the first and second integers is 1 less than 4 times the third. What three consecutive odd integers fit this description?

Answer 1

Consecutive odd integers are separated by 2, so the numbers are

n

n + 2

n + 4

The wording of the problem translates into

n(n + 2) = 4(n + 4) - 1

n² + 2n = 4n + 16 - 1

n² - 2n - 15 = 0

(n - 5)(n + 3) = 0

n = 5 or -3

There are 2 sets of odd integers that satisfy this: {5,7,9} and {-3,-1,1}. Test the answers.