Question

I don't remember how to solve problems like this one. Help!
The product of two numbers is 323 and the difference between them is 2.

What are the two numbers?

Answer 1

Nevermind got it. 19 and 17

Answer 2

xy= 323
x-y= 2 (we assume x is the bigger number)

rewrite the 2nd equation as
x= y+2

and use that expression to replace x in the first equation:
(y+2)y= 323
or
\[ y^2 +2y -323 = 0\]
now we factor that, knowing that the two numbers are close to each other and are whole numbers. the square root of 323 is about 18, so we can guess 17 and 19 at the facators
(y+19)(y-17) = 0
y= -19 or y= 17
ignore the negative answer.
y= 17
and x= y+2 , so x= 19