If a+b=2, \frac{1}{a}+\frac{1}{b}=2, then what is the value of a^3+b^3?

Explanation

From \frac{1}{a}+\frac{1}{b}=2, we get \frac{a+b}{ab}=2. Substituting a+b=2, we find ab=1. Using the identity a^3+b^3 = (a+b)^3 - 3ab(a+b) = 2^3 - 3(1)(2) = 8 - 6 = 2.

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