The sequence of values given by the iterative formula
${x_{n + 1}} = \frac{{7{x_n}}}{8} + \frac{5}{{2x_n^4}}$,
with initial value ${x_1} = 1.7$, converges to $\alpha $.
a) Use this iterative formula to determine $\alpha $ correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
b) State an equation that is satisfied by $\alpha $ and hence show that $\alpha = \sqrt[5]{{20}}$.
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