Answer: (1) \(\alpha^2 + \beta^2 = 18\) (2) \(\alpha^3 + \beta^3 = 50\)
\(a = 1, b = -2, c = -7\), so \(\alpha + \beta = 2\) and \(\alpha\beta = -7\).
(1) \(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 4 - 2(-7) = 4 + 14 = 18\)
(2) \(\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\)
\[= 8 - 3(-7)(2) = 8 + 42 = 50\]