1 The sequence of values given by the iterative formula $$x _ { n + 1 } = \frac { 4 } { x _ { n } ^ { 2 } } + \frac { 2 x _ { n } } { 3 }$$ with initial value \(x _ { 1 } = 2\), converges to \(\alpha\).

1. Use this iterative formula to find \(\alpha\) correct to 3 decimal places. Give the result of each iteration to 5 decimal places.
2. State an equation that is satisfied by \(\alpha\), and hence find the exact value of \(\alpha\).