(i)[2]
By plotting an appropriate pair of graphs, demonstrate that the equation $x^3 = 3 - x$ has exactly one real root.
(ii)[2]
Show that, if the real sequence defined by $x_{n+1} = \frac{2x_n^3 + 3}{3x_n^2 + 1}$ converges, then its limit is the root of the equation from part (i).
(iii)[3]
Use this iterative formula to find the root correct to 3 decimal places. Show every iteration to 5 decimal places.