SOLUTION: The product of two consecutive positive odd integers is 255. What are the integers?

Question 246795:
The product of two consecutive positive odd integers is 255. What are the integers?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Consecutive odd integers are 2 apart from each other. So if one odd integer is x then the next one is 2 more: x+2.

So to say "The product of two consecutive positive odd integers is 255" as a number sentence we would use:

To solve this we will start by simplifying:

This is a quadratic equation. So we will get one side equal to zero (by subtracting 255 from each side):

Now we either factor the left side and use the Zero Product Property or use the Quadratic Formula. I'll factor:

According to the Zero Product Property this product can be zero only if one of the factors is zero. So:
or
Solving these we get:
or

Rmemeber, that x represents the first of the two consecutive odd integers. x+2 represnts the second. So we get two pairs of consecutive odd integers:
15 and 17 (when x = 15)
and
-17 and -15 (when x = -17)
Since the problem doesn't exclude negative numbers both pairs of numbers are solutions to the problem.
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