The difference between two numbers is 2 and their product is 224. what are the numbers?

Let be the two numbers. We have two pieces of information:

(the difference between the two numbers is 2)

(their product is 224)

From the first equation, we can deduce

If we plug this expression in the second equation, we have

If you solve this equation with the usual quadratic formula you get the solutions

So, you have the following couple of solutions, recalling that x is 2 more than y:

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2