The product of two consecutive odd integers is 255. Find the integers.

15 and 17

Step-by-step explanation:

The product of two consecutive odd integers gives 255

Let the first number be x

Then the second number will be x+2

The product will be

x (x+2) = 255

x²+2x=255

x²+2x-255=0

We have a quadratic equation. We can either use factorisation method or formulae method. Let's use the factorisation, which is the most common method

x²+2x-255

We look for the two numbers which will give us + 2 by addition or subtraction and by multiplication will give us - 255. And that number is 17 and - 15

x²+17x-15x-255

(x+17) (x-15)

x gives 17 and 15