1.

1). \(\frac{{8\left( {13 - 5\sqrt 2 } \right)}}{{\left( {5 - 2\sqrt 2 } \right)}}\)2). \(\frac{{8\left( {13 - 5\sqrt 6 } \right)}}{{\left( {1 - 2\sqrt 6 } \right)}}\)3). \(\frac{{8\left( {1 - 5\sqrt 6 } \right)}}{{\left( {5 - 2\sqrt 6 } \right)}}\)4). \(\frac{{8\left( {13 - 5\sqrt 6 } \right)}}{{\left( {5 - 2\sqrt 6 } \right)}}\)

Answer»

ATQ, x = 2 - √6

$(\frac{1}{x} = \frac{1}{{2 - \sqrt 6 }})$

Now, putting the above values in place of x2, we get,

$(\begin{array}{L} \Rightarrow {\LEFT( {2 - \sqrt 6 } \right)^2} + \frac{{12}}{{{{\left( {2 - \sqrt 6 } \right)}^2}}}\\ \Rightarrow 4 + 6 - 2 \TIMES 2 \times \sqrt 6+ \frac{{12}}{{4 + 6 - 2 \times 2 \times \sqrt 6 }}\\ \Rightarrow 10 - 4\sqrt 6+ \frac{{12}}{{10 - 4\sqrt 6 }}\\ \Rightarrow \frac{{{{\left( {10 - 4\sqrt 6 } \right)}^2} + 12}}{{10 - 4\sqrt 6 }}\\ \Rightarrow \frac{{{{\left( {10 - 4\sqrt 6 } \right)}^2} + 12}}{{10 - 4\sqrt 6 }}\\ \Rightarrow \frac{{100 + 16 \times 6 - 2 \times 10 \times 4\sqrt 6+ 12}}{{10 - 4\sqrt 6 }}\\ \Rightarrow \frac{{208 - 80\sqrt 6 }}{{10 - 4\sqrt 6 }}\\\therefore \frac{{8(13 - 5\sqrt {6)} }}{{\left( {5 - 2\sqrt 6 } \right)}}\end{array})$


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