1 The roots of the cubic equation \(x ^ { 3 } + 2 x ^ { 2 } - 3 = 0\) are \(\alpha , \beta\) and \(\gamma\).
- By using the substitution \(y = \frac { 1 } { x ^ { 2 } }\), find the cubic equation with roots \(\frac { 1 } { \alpha ^ { 2 } } , \frac { 1 } { \beta ^ { 2 } }\) and \(\frac { 1 } { \gamma ^ { 2 } }\).
- Hence find the value of \(\frac { 1 } { \alpha ^ { 2 } } + \frac { 1 } { \beta ^ { 2 } } + \frac { 1 } { \gamma ^ { 2 } }\).
- Find also the value of \(\frac { 1 } { \alpha ^ { 2 } \beta ^ { 2 } } + \frac { 1 } { \beta ^ { 2 } \gamma ^ { 2 } } + \frac { 1 } { \gamma ^ { 2 } \alpha ^ { 2 } }\).