186k views
4 votes
If x + y = 12 and x * y = -360 what are the values of x and y

User Ryohei
by
8.3k points

1 Answer

6 votes

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...

User Erk
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories