2 The sequence of values given by the iterative formula
$$x _ { n + 1 } = \frac { 7 x _ { n } } { 8 } + \frac { 5 } { 2 x _ { n } ^ { 4 } }$$
with initial value \(x _ { 1 } = 1.7\), converges to \(\alpha\).
- Use this iterative formula to determine \(\alpha\) correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
- State an equation that is satisfied by \(\alpha\) and hence show that \(\alpha = \sqrt [ 5 ] { 20 }\).