a + b root 11 is equal to 5 + root 11 upon 3 minus 2 root 11
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tiger009:
\Rightarrow a + b\sqrt {11} = \frac{{5 + \sqrt {11} }}{{3 - 2\sqrt {11} }} \times \frac{{3 + 2\sqrt {11} }}{{3 + 2\sqrt {11} }} \hfill \\
\Rightarrow a + b\sqrt {11} = \frac{{\left( {5 + \sqrt {11} } \right) \times \left( {3 + 2\sqrt {11} } \right)}}{{\left( {3 - 2\sqrt {11} } \right) \times \left( {3 + 2\sqrt {11} } \right)}} \hfill \\
\Rightarrow a + b\sqrt {11} = \frac{{15 + 10\sqrt {11} + 3\sqrt {11} + 2 \times 11}}{{{3^2} - {{\left( {2\sqrt {11} } \right)}^2}}} \hfill \\
\Rightarrow a + b\sqrt {11} = \frac{{\left( {15 + 22} \right) + \left( {10 + 3} \right)\sqrt {11} }}{{9 - \left( {4 \times 11} \right)}} \hfill \\
\Rightarrow a + b\sqrt {11} = \frac{{37 + 13\sqrt {11} }}{{9 - 44}} \hfill \\
\Rightarrow a + b\sqrt {11} = \frac{{37}}{{ - 35}} + \frac{{13\sqrt {11} }}{{ - 35}} \hfill \\
\Rightarrow a + b\sqrt {11} = - \frac{{37}}{{35}} + \left( {\frac{{ - 13\sqrt {11} }}{{35}}} \right) \hfill \\
{\text{On comparision, we get}} \hfill \\
a = - \frac{{37}}{{35}}\,\& \,b\, = \,\frac{{ - 13\sqrt {11} }}{{35}} \hfill \\
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