The system of equations is:

         x + y = 15
            xy = 15

Solve the first for y and substitute in the second:

             y = 15-x
       x(15-x) = 15
      15x - x² = 15
 15x - x² - 15 = 0
-x² + 15x - 15 = 0
 x² - 15x + 15 = 0









And by symmetry, we may interchange x and y and get the
same result.



The irrational parts of x and y must have opposite signs
otherwise their sum could not be 15.

Answer: 

So there are two numbers that such that their sum and product
are both 15.

Checking their sum:










Checking their product:











Edwin