Question

How do you find three consecutive odd integers such that the sum of all three is 36 less than the product of the smaller two?

Answer 1

`7, 9, 11`.

Explanation:

Let the numbers be `x`, `x + 2` and `x + 4`

`x + (x + 2) + (x + 4) = x(x + 2) - 36`

`x + x + 2 + x + 4 = x^2 + 2x - 36`

`3x + 6 = x^2 + 2x- 36`

`0 = x^2 - x - 42`

`0 = (x - 7)(x + 6)`

`x = 7 and -6`

Since the numbers have to be odd, the numbers are `7`, `9` and `11`.

Hopefully this helps!