Given that \(2 \ln ( x + 1 ) + \ln x = \ln ( x + 9 )\), show that \(x = \sqrt { \frac { 9 } { x + 2 } }\).
It is given that the equation \(x = \sqrt { \frac { 9 } { x + 2 } }\) has a single root.
Show by calculation that this root lies between 1.5 and 2.0.
Use an iterative formula, based on the equation in part (b), to find the root correct to 3 significant figures. Give the result of each iteration to 5 significant figures.