2 In this question you must show detailed reasoning.
Express \(\frac { 8 + \sqrt { 7 } } { 2 + \sqrt { 7 } }\) in the form \(a + b \sqrt { 7 }\), where \(a\) and \(b\) are integers.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{808e5492-febe-434f-91b8-9b2888b17fcb-04_704_912_178_694}
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\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of a curve \(C\) and a straight line \(l\).
Given that
- \(C\) has equation \(y = \mathrm { f } ( x )\) where \(\mathrm { f } ( x )\) is a quadratic expression in \(x\)
- \(C\) cuts the \(x\)-axis at 0 and 6
- \(l\) cuts the \(y\)-axis at 60 and intersects \(C\) at the point \(( 10,80 )\)
use inequalities to define the region \(R\) shown shaded in Figure 3.
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