3．Given that \(\phi = \frac { 1 } { 2 } ( \sqrt { 5 } + 1 )\) ，
（a）show that
（i）\(\phi ^ { 2 } = \phi + 1\)
（ii）\(\frac { 1 } { \phi } = \phi - 1\)
（b）The equations of two curves are $$\begin{array} { r l r l } y & = \frac { 1 } { x } & x > 0
\text { and } & y & = \ln x - x + k & x > 0 \end{array}$$ where \(k\) is a positive constant．
The curves touch at the point \(P\) ．
Find in terms of \(\phi\)
（i）the coordinates of \(P\) ，
（ii）the value of \(k\) ．