Question

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

Answer 1

Let $x,y$ be the two numbers. We have two pieces of information:

$x-y=2$ (the difference between the two numbers is 2)

$xy=224$ (their product is 224)

From the first equation, we can deduce $x=y+2$

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

$xy = (y+2)y = 224 \iff y^2+2y-224 =0$

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

$y=-16,\quad y=14$

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

$\begin{cases} x = -14\\y=-16\end{cases},\quad\begin{cases} x = 16\\y=14\end{cases}$