What two numbers multiply to equal 2 but add up to equal 10?

Answer 1

12

Answer 2

Proceeding as in answer 1, since x + y = 10, x = 10 - y . When we plug x = 10 - y into xy = 2, we get (10 - y)y = 2, which works out to y2 - 10y + 2 = 0. The quadratic formula (which is derived by completing the square) gives the solutions 5 + √23 and 5 - √23. Those are the two numbers.

Answer 1

Let's call the two numbers x and y. We know that

xy = 2

and that

x + y = 10.

Solving the second equation for x gives us x = y - 10. Plug that into the first equation: (y-10)y = 10. You can then use the quadric formula or complete the square to solve for y. (y2 - 10y - 10 = 0). y ends up being 5 + √35 or 5 - √35.

So the two numbers are 5 + √35 and 5 - √35.