8. The point \(P ( 1 , a )\) lies on the curve with equation \(y = ( x + 1 ) ^ { 2 } ( 2 - x )\).
- Find the value of \(a\).
- On the axes below sketch the curves with the following equations:
- \(y = ( x + 1 ) ^ { 2 } ( 2 - x )\),
- \(y = \frac { 2 } { x }\).
On your diagram show clearly the coordinates of any points at which the curves meet the axes.
- With reference to your diagram in part (b) state the number of real solutions to the equation
$$( x + 1 ) ^ { 2 } ( 2 - x ) = \frac { 2 } { x } .$$
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