Question

if any give incarrect or say I don't know so I report and you lose your points​

Answer 1

Answer:

$if \: x = 5 - 2 \sqrt{6}$

$then \frac{1}{x } = \frac{1}{5 - 2 \sqrt{6} }$

$rationalize \: these$

$\frac{1}{x} = \frac{5 + 2 \sqrt{6} }{5 - 2 \sqrt{6 } \times 5 + 2 \sqrt{6} }$

$\frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 24}$

$\frac{1}{x} = 5 + 2 \sqrt{6}$

$so \: \: x + \frac{1}{x} =5 - 2 \sqrt{6} + 5 - 2 \sqrt{6}$

$x + \frac{1}{x} = 10$

$if \: we \: take \: \sqrt{} \: in \: both \: side$

$\sqrt{x + \frac{1}{x} } = \sqrt{10}$

$\sqrt{x} + \sqrt{ \frac{1}{x} } = \sqrt{10}$

$\sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{10}$