Question

if x=2+under root 3 find, under root x+1/under root x

Answer 1

$x = 2 + \sqrt{3} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } = \frac{2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3}) } \\ = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3}$
$x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$
${( \sqrt{x} + \frac{1}{ \sqrt{x} } )}^{2} = x + \frac{1}{x} + 2 \\ = 4 + 2 = 6 \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{6}$