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If x + y = xy = 3, what is x^3 + y^3?

I have tried solving this using algebra alone, but my teacher told me to use complex numbers, and I don't know how to start. Can someone please guide me to the solution to this problem?

Thanks
Kevin

1 answer

note that

(x+y)^2 = x^2+2xy+y^2
x^3 + y^3 = (x+y)(x^2-xy+y^2)

Now just plug in what you know.