Question

Pls help me with this I beg you

Answer 1

Step-by-step explanation:

$= x + \frac{1 }{x} \\ = \frac{ {x}^{2} + 1 }{x} \\ = \frac{ {(8 - 4 \sqrt{3} )}^{2} + 1}{8 - 4 \sqrt{3} } \\ = \frac{64 + 48 - 64 \sqrt{3} + 1 }{8 - 4 \sqrt{3} } \\ = \frac{113 - 64 \sqrt{3} }{8 - 4 \sqrt{3} } \\ \\ \\ = \sqrt{x} + \frac{1}{ \sqrt{x} } \\ = \frac{x + 1}{ \sqrt{x} } \\ = \frac{8 - 4 \sqrt{3} + 1 }{ \sqrt{8 - 4 \sqrt{3} } } \\ = \frac{9 - 4 \sqrt{3} }{ \sqrt{8 - 4 \sqrt{3} } } \\ = \frac{9 - 4 \sqrt{3} }{2 \sqrt{2 - \sqrt{3} } }$