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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