The product of two consecutive odd integers is 782. What are the integers?

Call the smaller of the two odds = n

Call the next number in the sequence = n + 2

n * (n + 2) = 782 Remove the brackets.

n^2 + 2n = 782 Subract 782 from both sides.

n^2 + 2n - 782 = 0 We are going to have to factor this.

Discussion

This problem can't be done the way it is written. The product of an odd integer with another odd integer is and odd integer. There are no exceptions to this. So you need to give a number that has two factors very near it's square root for this question to work.

For example, you could use 783, (which factors) instead of 782.

Solve

n^2 + 2n - 783 = 0

(n + 29) (x - 27) = 0

Solution One

n - 27 = 0

n = 27

The two odd consecutive integers are 27 and 29.

Solution Two

n + 29 = 0

n = - 29

The two solution integers are - 29 and - 27 Notice that - 29 is smaller than - 27.