Question

If $x=9-4\sqrt{5}$ then , find the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$

Answer 1

$x=9-4\sqrt{5}$

$x=(5+4-2(2\left)\sqrt{5}\right)$

$x=(\sqrt{5}-2{)}^2$

$\sqrt{x}=\sqrt{5}-2$

$\Rightarrow \sqrt{x}+\frac{1}{\sqrt{x}}$

$\Rightarrow \sqrt{5}-2+\frac{1}{\sqrt{5}-2}$

$\Rightarrow \sqrt{5}-2+\sqrt{5}+2=2\sqrt{5}$.