Question

if the product of tow consective ood integers is 255,find the integers

Answer 1

Step-by-step explanation:

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:

%28x%29%2A%28x%2B2%29+=+255

To solve this we will start by simplifying:

x%5E2+%2B+2x+=+255

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

x%5E2+%2B+2x+-+255+=+0

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

%28x+-+15%29%28x%2B17%29+=+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%2B17+=+0

Solving these we get:

x+=+15 or x+=+-17

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.