SOLUTION: The product of two consecutive positive odd integers is ≤24. Find the numbers.

Algebra ->  Absolute-value -> SOLUTION: The product of two consecutive positive odd integers is ≤24. Find the numbers.      Log On


   

Question 847246: The product of two consecutive positive odd integers is ≤24. Find the numbers.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the smaller of the two. Then n+2 is the next odd integer.

n*(n+2) <= 24
n^2 +2n <=24
n^2 +2n - 24 <=0
(n+6)(n-4)
<------ -6 --------------- 4 --------------->
Since the integers must be consecutive and odd, we narrow down the possibilities
of the smaller number to either 1 or 3.
So the only possible matches are 1 and 3 or 3 and 5.