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