Question

The product of two consecutive odd integers is 899. How do you find the integers?

Answer 1

899 is just 1 less than 900. And 900 is the square of 30. And 1 is the square of 1. So 899 is the difference of two squares.

Explanation:

We have a special product here, of the form:
`(A-B)(A+B)=A^2-B^2`

If we take `30and1` for `AandB`:
`(30-1)(30+1)=30^2-1^2=900-1=899` BINGO!

So the answer is `29and31`

Note : of course `-29and-31` also count as a solution.