SOLUTION: Solve the system algebraically. { x^2 - 4y^2 = 5 xy = 3

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Question 918087: Solve the system algebraically.
{ x^2 - 4y^2 = 5
xy = 3
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system algebraically.
{ x^2 - 4y^2 = 5
xy = 3
***
x^2-4y^2=5
xy=3
y=3/x
..
x^2-4(3/x)^2=5
x^2-4(9/x^2)=5
x^2-36/x^2=5
lcd:x^2
x^4-5x^2-36=0
(x^2-9)(x^2+4)
(x+3)(x-3)(x^2+4)
x=-3
or
x=3
or
x^2+4=0
x^2=-4
x=±√(-4)=±√4*√-1=±2i
solution: x=-3, 3, ±2i