The cubic equation \(x^{3}-p x-q=0\), where \(p\) and \(q\) are constants, has roots \(\alpha, \beta, \gamma\). Show that
(i) \(\alpha^{2}+\beta^{2}+\gamma^{2}=2 p\),

(ii) \(\alpha^{3}+\beta^{3}+\gamma^{3}=3 q\),

(iii) \(6\left(\alpha^{5}+\beta^{5}+\gamma^{5}\right)=5\left(\alpha^{3}+\beta^{3}+\gamma^{3}\right)\left(\alpha^{2}+\beta^{2}+\gamma^{2}\right)\).