(i)[2]
Verify by calculation that the cubic equation $x^3 - 2x^2 + 5x - 3 = 0$ has a root between $x = 0.7$ and $x = 0.8$.
(ii)[2]
Show that this root also obeys an equation of the form $x = \frac{ax^2 + 3}{x^2 + b}$, with the values of $a$ and $b$ still to be found.
(iii)[3]
With these values of $a$ and $b$, apply the iterative formula $x_{n+1} = \frac{ax_n^2 + 3}{x_n^2 + b}$ to find the root correct to $2$ decimal places. Show the result of each iteration to $4$ decimal places.