(a) By sketching a suitable pair of graphs, show that the equation \(\ln x = 3x - x^2\) has one real root.

(b) Verify by calculation that the root lies between 2 and 2.8.

(c) Use the iterative formula \(x_{n+1} = \sqrt{3x_n - \ln x_n}\) to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.