0606 P11 - Jun 2021 - Q8 - 8 marks
7947
Do not use a calculator in this question.
A curve has equation
\(y=(2-\sqrt3)x^2+x-1.\)
The \(x\)-coordinate of a point \(A\) on the curve is
\(\frac{\sqrt3+1}{2-\sqrt3}.\)
(a) Show that the coordinates of \(A\) can be written in the form \((p+q\sqrt3,r+s\sqrt3)\), where \(p,q,r\) and \(s\) are integers.
(b) Find the \(x\)-coordinate of the stationary point on the curve, giving your answer in the form \(a+b\sqrt3\), where \(a\) and \(b\) are rational numbers.
