The sequence of values given by the iterative formula

\(x_{n+1} = \frac{x_n(x_n^3 + 100)}{2(x_n^3 + 25)}\),

with initial value \(x_1 = 3.5\), converges to \(\alpha\).

1. Use this formula to calculate \(\alpha\) correct to 4 decimal places, showing the result of each iteration to 6 decimal places.
2. State an equation satisfied by \(\alpha\) and hence find the exact value of \(\alpha\).