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