Description for Correct answer:
\( \Large x + \frac{1}{x} = 6 \)

On squaring both sides, we get

\( \Large \left(x + \frac{1}{x}\right)^{2} = \left(6\right)^{2} \)

\( \Large x^{2} + \frac{1}{x^{2}} + 2 = 36 \)

\( \Large x^{2} + \frac{1}{x^{2}} = 34 \)

On squaring both sides, we get

\( \Large \left(x^{2} + \frac{1}{x^{2}}\right)^{2} = \left(34\right)^{2} \)

\( \Large x^{4} + \frac{1}{x^{4}} + 2 = 1156 \)

\( \Large x^{4} + \frac{1}{x^{4}} = 1154 \)