The curve is given by $y = 2x + \frac{12}{x}$, while the line has equation $y + x = k$, where $k$ is a constant.
(i)[3]
Find the values of $k$ for which the line does not meet the curve.
(ii)[3]
When $k = 15$, the curve meets the line at $A$ and $B$. Find the coordinates of $A$ and $B$.
(iii)[3]
Find the equation of the perpendicular bisector of the segment joining $A$ and $B$.
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