A) 2
B) 4
C) \[2\sqrt{3}\]
D) \[\sqrt{3}\]
Correct Answer: C
Solution :
(c): \[={{a}^{2}}+\frac{1}{{{a}^{2}}}=14={{a}^{2}}-2.a.\frac{1}{a}+\frac{1}{{{a}^{2}}}=14-2\] \[\Rightarrow {{\left( a-\frac{1}{a} \right)}^{2}}=12\] \[\Rightarrow a-\frac{1}{a}=\sqrt{12}=2\sqrt{3}\].
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