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