A) \[2\sqrt{6}\]
B) \[2\sqrt{5}\]
C) \[20\]
D) \[24\]
Correct Answer: C
Solution :
\[x=\sqrt{6}+\sqrt{5}\] \[\therefore \]\[\frac{1}{x}=\frac{1}{\sqrt{6}+\sqrt{5}}\] \[=\frac{(\sqrt{6}-\sqrt{5})}{(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5})}=\sqrt{6}-\sqrt{5}\] \[\therefore \] \[({{x}^{2}}+\frac{1}{{{x}^{2}}}-2)={{(x-\frac{1}{x})}^{2}}\]
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