2 The sequence defined by
$$x _ { 1 } = 3 , \quad x _ { n + 1 } = \sqrt [ 3 ] { 31 - \frac { 5 } { 2 } x _ { n } }$$
converges to the number \(\alpha\).
- Find the value of \(\alpha\) correct to 3 decimal places, showing the result of each iteration.
- Find an equation of the form \(a x ^ { 3 } + b x + c = 0\), where \(a\), \(b\) and \(c\) are integers, which has \(\alpha\) as a root.