A) 2
B) 3
C) 4
D) 6
Correct Answer: C
Solution :
[c] \[\because x=\sqrt{7+4\sqrt{3}}\] \[x=\sqrt{{{(2)}^{2}}+{{(3)}^{2}}+2.2\sqrt{3}}=\sqrt{{{(2+\sqrt{3})}^{2}}}=2+\sqrt{3}\] \[\therefore \frac{1}{x}=\frac{1}{2+\sqrt{3}}=\frac{2-\sqrt{3}}{{{(2)}^{2}}-{{(\sqrt{3})}^{2}}}=2-\sqrt{3}\] \[\therefore x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4\] Hence, option [c] is correct.You need to login to perform this action.
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