No, I'm afraid it isn't 3

Algebra Level 2

If a+b=1a+b=1 and a2+b2=2a^{2}+b^{2}=2, what is a3+b3a^{3}+b^{3}? If your answer is xy\frac{x}{y}, where xx and yy are coprime positive integers, find x+yx+y.

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