A curve has equation $y = x \ln(8 - x)$. Its gradient is 1 at exactly one point, where $x = a$.
(i)[3]
Show that $a$ satisfies $x = 8 - \frac{8}{\ln(8 - x)}$.
(ii)[2]
Use calculation to confirm that $a$ lies between $2.9$ and $3.1$.
(iii)[3]
Use an iterative formula derived from the equation in part (i) to find $a$ correct to 2 decimal places. State each iterate to 4 decimal places.
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