Description for Correct answer:
\( \Large x = 7 - 4\sqrt{3} \)

\( \Large \frac{1}{x} => \frac{1}{7-4\sqrt{3}} \)

By ratonalisation,

\( \Large \frac{1}{x}=\frac{1}{7-4\sqrt{3}} \times \frac{7+4\sqrt{3}}{7+4\sqrt{3}} \)

= \( \Large \frac{7+4\sqrt{3}}{49-48}= 7 + 4\sqrt{3} \)

Therefore, \( \Large x+\frac{1}{x} = 7 - 4\sqrt{3} + 7 + 4\sqrt{3} \)

= 14