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.
\(a+b=7\)
\((a+b)^2=7^2\)
\(a^2+2ab+b^2=49\)
\((a+b)^3=7^3\)
\(a^3 + 3a^2b+3ab^2+b^3=343\)
\(3a^2b+3ab^2=301\)
\(a^2b+ab^2=\frac{301}{3}\)
\(ab(a+b)=\frac{301}{3}\)
\(ab(7)=\frac{301}{3}\)
\(ab = \frac{43}{3}\)
\(a^2 + 2ab + b^2 = 49\)
\(a^2 + \frac{86}{3} + b^2 = 49\)
\(a^2 + b^2 = 49 - \frac{86}{3} \)
\(a^2 + b^2 = \boxed{\frac{61}{3}}\)
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