# No, I'm afraid it isn't 3

Algebra Level 2

If $$a+b=1$$ and $$a^{2}+b^{2}=2$$, what is $$a^{3}+b^{3}$$? If your answer is $$\frac{x}{y}$$, where $$x$$ and $$y$$ are coprime positive integers, find $$x+y$$.

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