6 The cubic equation \(3 x ^ { 3 } - 9 x ^ { 2 } + 6 x + 2 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
- (a) Write down the values of \(\alpha + \beta + \gamma\) and \(\alpha \beta + \beta \gamma + \gamma \alpha\).
(b) Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\). - (a) Use the substitution \(x = \frac { 1 } { u }\) to find a cubic equation in \(u\) with integer coefficients.
(b) Use your answer to part (ii) (a) to find the value of \(\frac { 1 } { \alpha } + \frac { 1 } { \beta } + \frac { 1 } { \gamma }\).