A) \[a\sqrt{3}\]
B) \[\sqrt{3}\]
C) \[2\sqrt{2}\]
D) None of these
Correct Answer: B
Solution :
\[x=5+2\sqrt{6}\] \[\Rightarrow \] \[\sqrt{x}=\sqrt{5+2\sqrt{6}}=\sqrt{A}+\sqrt{B}\] \[\therefore \] \[x=5+2\sqrt{6}=A+B+2\sqrt{AB}\] \[\Rightarrow \] \[A+B=5,\,\,AB=6\] \[\Rightarrow \] \[A=3,\,\,B=2\] \[\Rightarrow \] \[\sqrt{x}=\sqrt{3}+\sqrt{2}\] \[\therefore \] \[\frac{\sqrt{x}-1}{\sqrt{x}}=\frac{\sqrt{3}+\sqrt{2-1}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\] \[=1-\sqrt{3}+\sqrt{2}=1-(\sqrt{3}-\sqrt{2})\]
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