\(\left\{{}\begin{matrix}x_1+x_2=\dfrac{-\left(-3\right)}{2}=\dfrac{3}{2}\\x_1x_2=\dfrac{-7}{2}\end{matrix}\right.\)
a: \(x_1^2+x_2^2=\left(x_1+x_2\right)^2-2x_1x_2\)
\(=\dfrac{9}{4}-2\cdot\dfrac{-7}{2}=\dfrac{9}{4}+7=\dfrac{37}{4}\)
b: \(x_1^3+x_2^3=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)\)
\(=\dfrac{27}{8}-3\cdot\dfrac{3}{2}\cdot\dfrac{-7}{2}\)
\(=\dfrac{27}{8}+\dfrac{63}{4}\)
\(=\dfrac{153}{8}\)
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