If x + y = 12 and x * y = -360 what are the values of x and y

Step-by-step explanation:

x + y = 12

x × y = -360

we need to transform one equation into an identity of one variable being expressed by the other variable.

e.g. the first equation gives us

x = -y + 12

and then we use that in the second equation :

(-y + 12) × y = -360

-y² + 12y = -360

y² - 12y - 360 = 0

the general solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = y

a = 1

b = -12

c = -360

y = (12 ± sqrt(144 - 4×1×-360))/2 =

= (12 ± sqrt(144 + 1440))/2 = (12 ± sqrt(1584))/2 =

= 6 ± sqrt(1584/4) = 6 ± sqrt(396) = 6 ± sqrt(36×11) =

= 6 ± 6×sqrt(11)

y1 = 6 + 6×sqrt(11) = 25.89974874...

y2 = 6 - 6×sqrt(11) = -13.89974874...

x1 = -y1 + 12 = -13.89974874...

x2 = -y2 + 12 = 25.89974874...

so, we see, they are interchangeable.

the solution is either

x = 25.89974874...

and

y = -13.89974874...

or

x = -13.89974874...

and

y = 25.89974874...

ok thats very interesting