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)


`(-b- √(b*b-4a*c) )/(2a)`

`(3- √(3*3-4*(-12)) )/(2) = (3- √(9+48) )/(2) = (3- √(57) )/(2)`


So this would be the solution, where the other number would be

`3-(3- √(57) )/(2)= (6)/(2)-(3- √(57) )/(2)=(3- √(57) )/(2)`

The other solution would be the following one;

x=
`(3+√(57) )/(2)`, y=
`1(1+√(57) )/(2)`