A) \[\frac{1}{2}\]
B) \[\sqrt{3}\]
C) 3
D) \[3\sqrt{3}\]
Correct Answer: D
Solution :
[d] \[x=3\sqrt{3}+\sqrt{26}\] \[\frac{1}{x}=\frac{1}{3\sqrt{3}+\sqrt{26}}\times \frac{3\sqrt{3}-\sqrt{26}}{3\sqrt{3}-\sqrt{26}}\] \[\frac{3\sqrt{3}-\sqrt{26}}{(27)-(26)}=3\sqrt{3}-\sqrt{26}\] \[\therefore \,\,\,\frac{1}{2}\left( x+\frac{1}{x} \right)=\frac{1}{2}\left[ (3\sqrt{3}+\sqrt{26})+(3\sqrt{3}-\sqrt{26}) \right]\] \[=\frac{1}{2}\times 6\sqrt{3}=3\sqrt{3}\]
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