Question 246795
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.<br>
So to say "The product of two consecutive positive odd integers is 255" as a number sentence we would use:
{{{(x)*(x+2) = 255}}}<br>
To solve this we will start by simplifying:
{{{x^2 + 2x = 255}}}
This is a quadratic equation. So we will get one side equal to zero (by subtracting 255 from each side):
{{{x^2 + 2x - 255 = 0}}}
Now we either factor the left side and use the Zero Product Property or use the Quadratic Formula. I'll factor:
{{{(x - 15)(x+17) = 0}}}
According to the Zero Product Property this product can be zero only if one of the factors is zero. So:
{{{x-15 = 0}}} or {{{x+17 = 0}}}
Solving these we get:
{{{x = 15}}} or {{{x = -17}}}<br>
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.