10. (a) On the axes below sketch the graphs of
- \(y = x ( 4 - x )\)
- \(y = x ^ { 2 } ( 7 - x )\)
showing clearly the coordinates of the points where the curves cross the coordinate axes.
(b) Show that the \(x\)-coordinates of the points of intersection of
$$y = x ( 4 - x ) \text { and } y = x ^ { 2 } ( 7 - x )$$
are given by the solutions to the equation \(x \left( x ^ { 2 } - 8 x + 4 \right) = 0\)
The point \(A\) lies on both of the curves and the \(x\) and \(y\) coordinates of \(A\) are both positive.
(c) Find the exact coordinates of \(A\), leaving your answer in the form ( \(p + q \sqrt { } 3 , r + s \sqrt { } 3\) ), where \(p , q , r\) and \(s\) are integers.
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