Question

please tell me the answer... please​

Answer 1

Answer:

that's the step by step explanation

Answer 2

Explanation:

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

$\therefore \: \frac{1}{x} = \frac{1}{2 \sqrt{6} }$

On rationalizing the denominator,

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

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

$\scriptsize\frac{1}{x} = \frac{5 + 2 \sqrt{6} }{( {5})^{2}- ( {2 \sqrt{6} })^{2} } \: [ \because \: (a + b)(a - b) = {a}^{2} - {b}^{2}]$

$\frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 4 \times 6}$

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

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

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

$= 5 + 5 - 2 \sqrt{6} + 2 \sqrt{6}$

$= 10$

I hope it is helpful