The sequence of values given by the iterative formula

\(x_{n+1} = \frac{2x_n^6 + 12x_n}{3x_n^5 + 8}\),

with initial value \(x_1 = 2\), converges to \(\alpha\).

(i) Use the formula to calculate \(\alpha\) correct to 4 decimal places. Give the result of each iteration to 6 decimal places. [3]

(ii) State an equation satisfied by \(\alpha\) and hence find the exact value of \(\alpha\). [2]