Question

Plzzz solve it..........

Answer 1

Here is your solution

Answer 2

$Given : x = 5 + 2\sqrt{6}$

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

$=> \frac{5 - 2\sqrt{6}}{(5)^2 - (2\sqrt{6})^2 }$

$=> \frac{5 - 2\sqrt{6}}{25 - 24}$

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

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

Now,

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

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

Add 2 from both sides, we get

$= > x + \frac{1}{x} + 2 = 12$

$= > (\sqrt{x} + \frac{1}{\sqrt{x}})^2 = (2\sqrt{3})^2$

$= > \sqrt{x} + \frac{1}{\sqrt{x}} = 2\sqrt{3}$

Hope this helps!