Let x and y be complex numbers. If x + y = 2 and xy = 5 - x^2 - y^2, then what is x^2 + y^2?
x + y = 2
square both sides
x^2 + 2xy + y^2 = 4
x^2 + y^2 = 4 - 2xy
xy = 5 -x^2 - y^2
xy = 5 - (x^2 + y^2)
So
x^2 + y^2 = 4 -2xy
x^2 + y^2 = 4 - 2 [ 5 - (x^2 + y^2) ]
x^2 + y^2 = 4 - 10 + 2(x^2 + y^2)
-3(x^2 + y^2) = -6
x^2 + y^2 = -6 / -3 = 2
+782 
