If a + b = 7 and a^3 + b^3 = 42, what is the value of the sum a^2 + b^2? Express your answer as a common fraction.
a^3 + b^3 = 42
(a+b)(a^2 - ab + b^2) = 42
a^2 - ab + b^2 = 6
(a+b)^2 - 3ab = 6
49 - 3ab = 6
ab = 43/3
a^2 - 43/3 + b^2 = 6
a^2 + b^2 = 20 1/3
=^._.^=
