4 The sequence of values given by the iterative formula
$$x _ { n + 1 } = \sqrt { } \left( \frac { 1 } { 2 } x _ { n } ^ { 2 } + 4 x _ { n } ^ { - 3 } \right)$$
with initial value \(x _ { 1 } = 1.5\), converges to \(\alpha\).
- Use this iterative formula to find \(\alpha\) correct to 3 decimal places. Give the result of each iteration to 5 decimal places.
- State an equation that is satisfied by \(\alpha\) and hence find the exact value of \(\alpha\).