SOLUTION: If x^2 + y^2 = 40 and xy = 12, then x + y = A. 7. B. 8. C. 7 or −7. D. 8 or −8. E. None of these.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If x^2 + y^2 = 40 and xy = 12, then x + y = A. 7. B. 8. C. 7 or −7. D. 8 or −8. E. None of these.      Log On


   

Question 286767: If x^2 + y^2 = 40 and xy = 12, then x + y =
A. 7. B. 8. C. 7 or −7. D. 8 or −8. E. None of these.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 = 40
xy = 12 or x=12/y
Now replace x in the first equation with 12/y & solve for y.
(12/y)^2+y^2=40
144/y^2+y^2=40
(144+y^2*y^2)/y^2=40
144+y^4=40y^2
y^4-40y^2+144=0
(y^2-36)(y^2-4)=0
(y+6)(y-6)(y+2)(y-2)=0
y+6=0
y=-6 ans.
y-6=0
y=6 ans.
y+2=0
y=-2 ans.
y-2=0
y=2 ans.
x=12/+-6=+-2 ans.
x=12/+-2=+-6 ans.
Proof:
262+6^2=40
4+36=40
then x + y =2+6=8 ans.
x+y=-2-6=-8 ans.