2 The sequence of values given by the iterative formula
$$x _ { n + 1 } = \frac { 2 x _ { n } ^ { 6 } + 12 x _ { n } } { 3 x _ { n } ^ { 5 } + 8 }$$
with initial value \(x _ { 1 } = 2\), converges to \(\alpha\).
- Use the formula to calculate \(\alpha\) correct to 4 decimal places. Give the result of each iteration to 6 decimal places.
- State an equation satisfied by \(\alpha\) and hence find the exact value of \(\alpha\).