Question

what times what equals 12 but when you add those numbers together it equals 3

Answer 1

So, we can write it like this:

x+y=3
x*y=12
from the first we know that
x+y=3
y=3-x

so:

x*y=12 can be written as:
x*(x-3)=12

so x^2-3x=12

Actually this equation does not have a solution within the real numbers

but we can calculate:

x^2-3x-12=0

and if we use the quadratic formula, we will have:

(remember the quadratic formula is the following, where for us a=1,b=-3 and c=-12)

$\frac{-b- \sqrt{b*b-4a*c} }{2a}$
$\frac{3- \sqrt{3*3-4*(-12)} }{2} = \frac{3- \sqrt{9+48} }{2} = \frac{3- \sqrt{57} }{2}$


So this would be the solution, where the other number would be
$3-\frac{3- \sqrt{57} }{2}= \frac{6}{2}-\frac{3- \sqrt{57} }{2}=\frac{3- \sqrt{57} }{2}$

The other solution would be the following one;

x=$\frac{3+\sqrt{57} }{2}$, y=$1\frac{1+\sqrt{57} }{2}$