(i)[2]
By drawing a suitable pair of graphs, show that the equation $x^3 = 3 - x$ has one and only one real root.
(ii)[2]
Show that, if a sequence of real values defined by the iterative formula $x_{n+1} = \frac{2x_n^3 + 3}{3x_n^2 + 1}$ converges, then its limit is the root of the equation in part (i).
(iii)[3]
Use this iterative formula to determine the root correct to 3 decimal places. Give the result of each iteration to 5 decimal places.