A) \[\frac{61}{63}\]
B) \[\frac{67}{65}\]
C) \[\frac{65}{63}\]
D) \[\frac{69}{67}\]
Correct Answer: A
Solution :
(a): again ab = 1 \[a={{\left( \frac{\sqrt{5}-\sqrt{3}}{2} \right)}^{2}};b={{\left( \frac{\sqrt{5}+\sqrt{3}}{2} \right)}^{2}}\] Expression =\[\frac{{{\left( a-b \right)}^{2}}+ab}{{{\left( a+b \right)}^{2}}+ab}\] Expression=\[\frac{{{\left( -2\times \sqrt{15} \right)}^{2}}+1}{{{8}^{2}}-1}=\frac{61}{63}\left\{ \begin{align} & as(a-b)=-2\sqrt{15} \\ & and\,(a+b)=8 \\ \end{align} \right\}\]
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