3 The sequence of values given by the iterative formula
$$x _ { n + 1 } = \frac { 3 x _ { n } } { 4 } + \frac { 15 } { x _ { n } ^ { 3 } }$$
with initial value \(x _ { 1 } = 3\), converges to \(\alpha\).
- Use this iterative formula to find \(\alpha\) correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
- State an equation satisfied by \(\alpha\) and hence find the exact value of \(\alpha\).