What two numbers add up to equal 2 and multiply to equal -16?

Answer 1

-14

Answer 2

If we think of the numbers as "a" and "b", then we are told:

a + b = 2

a * b = -16

So we can solve either of those equations for either a or b:

a + b = 2

b = 2 - a

And then substitute that equation into the other one:

a * b = -16

a *(2 - a) = -16

And then solve for a:

2a - a2 = -16

a2 - 2a - 16 = 0

a2 - 2a + 1 = 17

(a - 1)2 = 17

a - 1 = ±√17

a = 1 ±√17

a ≈ {5.1231, -3.1231}

Now we can take those numbers, and plug them into one of our original equations to get the potential values of b:

b = 2 - a

b ≈ {-3.1231, 5.1231}

Which of course, gives us the reflection of our original set. In other words, the two numbers that meet these conditions are 1 - √17 and 1 + √17.