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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