What two numbers add to make 11 but multiply to make 40?

Answer 1

51

Answer 2

That isn't possible; at least, not with real numbers. The extreme case is 5.5 + 5.5 = 11, and 5.5 x 5.5 = 30.25. Any other combination of numbers that add up to 11 will have a product that's even less.

If you are interested in the complex solution to this problem, you can solve this with the quadratic formula. The Wolframalpha site gives the following solution, which is pressumably the only solution:

Input: a(11-a) = 40

Solution:

a1 = (1/2)(11-i root(-39))

a2 = (1/2)(11+i root(-39))

...where "i" is the imaginary unit, and root() is my way of writing "the square root of..."