A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
\[x=7-4\sqrt{3}\] \[\therefore \] \[\sqrt{x}=\sqrt{7-4\sqrt{3}}\] \[=\sqrt{7-2\times 2\times \sqrt{3}}\] \[=\sqrt{4+3-2\times 2\times \sqrt{3}}\] \[=\sqrt{{{(2-\sqrt{3})}^{2}}}=2-\sqrt{3}\] \[\therefore \] \[\frac{1}{\sqrt{x}}=\frac{1}{2-\sqrt{3}}\] \[=\frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2+\sqrt{3}}{4-3}\] \[=2+\sqrt{3}\] \[\therefore \] \[\sqrt{x}+\frac{1}{\sqrt{x}}\]\[=2-\sqrt{3}+2+\sqrt{3}=4\]
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