the product of two consecutive odd numbers is 323. find the numbers

Question

Word problem leading to quadratic equations

Answer 1

Let the numbers be 2n+1 and 2n-1, an even number -1 and the same even number+1.  Two successive odd numbers.

Their product is (2n+1)(2n-1)=4n²-1=323

4n²=324,  n²=81, n=9 gives 2n-1=17, 2n+1=19

                           n=-9 gives 2n-1=-19, 2n+1=-17

The problem says nothing about the restriction to positive integers.

Answer 2

If you haven't learned quadratic equations yet then you are probably supposed to do this by trial and error.  

 

I will give you a hint - you might want to try numbers near the square root of 323, which is ~ 17.97.