What multiplies to 30 and adds up to 1?

Answer 1

31

Answer 2

We can write and solve a system of equations.

xy = 30

x + y = 1

And thus, y = 1 - x, so we can substitute.

x(1 - x) = 30

x - x2 = 30

-x2 + x - 30 = 0, or:

x2 - x + 30 = 0

Using the quadratic formula to solve gives us our roots, which are complex numbers: 1/2 (1 - i√119) and 1/2 (1 + i√119)

We can substitute these into the original equation to find our other number; rather conveniently, thanks to the way complex numbers work, whichever one you do not choose ends up being the solution, so the numbers in question are those two. Not the nicest solution ever, but it's the solution.