3 The equation \(x ^ { 5 } - 3 x ^ { 3 } + x ^ { 2 } - 4 = 0\) has one positive root.
- Verify by calculation that this root lies between 1 and 2 .
- Show that the equation can be rearranged in the form
$$\left. x = \sqrt [ 3 ] { ( } 3 x + \frac { 4 } { x ^ { 2 } } - 1 \right)$$
- Use an iterative formula based on this rearrangement to determine the positive root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.