Question

please solve this question

Answer 1

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

It can be written as,

$=> x = 3 + 2 + 2\sqrt{6}$

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

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

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

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$=>\frac{1}{\sqrt{x}}$

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

$=>\frac{\sqrt{3} -\sqrt{2}}{(\sqrt{3})^2 - (\sqrt{2})^2}$

$=>\frac{\sqrt{3} -\sqrt{2}} {3 - 2}$

$=>\sqrt{3} -\sqrt{2}$

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Therefore:

$=>\sqrt{x}  +\frac{1}{\sqrt{x}}$

$=>\sqrt{3} +\sqrt{2} +\sqrt{3} -\sqrt{2}$

$=> \boxed{2\sqrt{3}}$

Hope it helps!