Question

Please solve this fastly

Answer 1

$\textbf { HEY MATE }$

$\textbf { your answer is --}$

Given, x = 5-2√6

so, 1/x = 1/(5-2√6) = 5+2√6 ( rationalize it)

now,
${x}^{2} + \frac{1}{x} \\ \\ = {(5 - 2 \sqrt{6)} }^{2} + 5 + 2 \sqrt{6} \\ \\ = 25 + 24 - 20 \sqrt{6} + 5 + 2 \sqrt{6} \\ \\ = 54 - 18 \sqrt{6}$

$\textbf { HOPE IT HELP YOU}$