What are the numbers with a sum of 12 and a product of 36?

Answer 1

The two numbers are 6 and 6 (proof below).

1. x + y = 12

2. x * y = 36

Rewriting 1. gives x = -y + 12.

Substituting 1. into 2. gives:

3. (-y + 12) * y = 36

-y2 + 12y = 36

-y2 + 12y - 36 = 0

Substituting into the quadratic equation:

(-b + or - (b2 - 4ac)1/2) / 2a gives:

(-12 + or - (122 - (4 * -1 * -36))1/2) / 2 * -1

= (-12 + or - (144 - 144)1/2) / -2

= (-12 + or - 0) / -2

= 6.

Thus the two roots of the quadratic are 6 & 6.