Solve this problem as a quadratic equation. The difference between two positive numbers is 5. Their product is 104 find the numbers.

The best way to do this is to find the factors of 104. For this I got 1, 2, 4, 8, 13, 26, 52 and 104. From this, you are then able to look at the two that have a difference of five, which in this case, is 8 and 13. You should then double check that when these are multipled, they are equal to 104, which they are. I'm not 100% sure if this is the answer that you are looking for, but the two numbers are 8 and 13

Let's call the smaller number x:

y-x=5

xy=104

y-x=5 can be rewritten as y=x+5

Substituting this into the second equation gives:

x (x+5) = 104

x^2+5x=104

x^2+5x-104=0

Then simply solve as a quadratic:

x^2+13x-8x-104=0

x (x+13) - 8 (x+13) = 0

(x-8) (x+13) = 0

x=8,-13

the question said the numbers are positive, so x=8

if x=8,

y=x+5

y=13

So the two numbers are 8 and 13.