Question

X=(5+2✓6),the show that ✓x+1/✓x=2✓3

Answer 1

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

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

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

$\frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{3} + \sqrt{2} } \\ \: \: \ = : \frac{1}{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3 } - \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

$= \frac{ \sqrt{3} - \sqrt{2} }{1}$

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