6 The curve with equation \(y = \frac { 6 } { x ^ { 2 } }\) intersects the line \(y = x + 1\) at the point \(P\).
- Verify by calculation that the \(x\)-coordinate of \(P\) lies between 1.4 and 1.6.
- Show that the \(x\)-coordinate of \(P\) satisfies the equation
$$x = \sqrt { } \left( \frac { 6 } { x + 1 } \right)$$
- Use the iterative formula
$$x _ { n + 1 } = \sqrt { } \left( \frac { 6 } { x _ { n } + 1 } \right)$$
with initial value \(x _ { 1 } = 1.5\), to determine the \(x\)-coordinate of \(P\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.