Paper 1 October/November 2011 MATHEMATICS (9709/13) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

The diagram shows parts of the curves $y = 9 - {x^3}$ and $y = \frac{8}{{{x^3}}}$ and their points of intersection $P$ and $Q$. The x-coordinates of $P$ and $Q$ are $\alpha $ and $b$ respectively.
a) Show that $x = \alpha $ and $x = b$ are roots of the equation ${x^6} - 9{x^3} + 8 = 0$. Solve this equation and hence state the value of $\alpha $ and the value of $b$.
b) Find the area of the shaded region between the two curves.
c) The…