Edexcel P1 2023 October — Question 8

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2023
SessionOctober
TopicSimultaneous equations

  1. 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 $$y = x ^ { 3 } - \frac { 7 } { 2 } x - 5$$
  1. 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 \(Q\)
  2. find, using algebra, the exact distance \(P Q\)