- In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
The curve \(C _ { 1 }\) has equation
$$x y = \frac { 15 } { 2 } - 5 x \quad x \neq 0$$
The curve \(C _ { 2 }\) has equation
$$y = x ^ { 3 } - \frac { 7 } { 2 } x - 5$$
- Show that \(C _ { 1 }\) and \(C _ { 2 }\) meet when
$$2 x ^ { 4 } - 7 x ^ { 2 } - 15 = 0$$
Given that \(C _ { 1 }\) and \(C _ { 2 }\) meet at points \(P\) and \(Q\)
- find, using algebra, the exact distance \(P Q\)