What numbers multiply to get 1008 and add to get 12?

Answer 1

1020

Answer 2

This brings you into the realm of complex numbers.

Let the two numbers be a and b.

Then, a + b = 12....Equation (1)

and, ab = 1008 .....so b = 1008/a

Substituting for b in Equation (1)

a + 1008/a = 12...........now multiply throughout by a and equate to zero.

a2 -12a + 1008 = 0

This can be solved using the quadratic formula

a = [12 ± √ (144 - 4032)] ÷ 2 = 6 ± i31.177 (3dp)

The two (complex) numbers are 6 + i31.177 and 6 - i31.177.

Check : (6 + i31.177) + (6 - i31.177) = 12

(6 + i31.177)(6 - i31.177) = 36 + 972 = 1008