Question

If x=1+root2, find the value of x+1/x

Answer 1

Step-by-step explanation:

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

LHS

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

Substitute the Value of X

$\frac{1}{ \sqrt{2} } + \frac{1}{ \frac{1}{ \sqrt{2} } }$

$\frac{1}{ \sqrt{2} } + \sqrt{2}$

Take LCM

$\frac{1 + 2}{ \sqrt{2} }$

$\frac{3}{ \sqrt{2} }$

$\frac{3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\frac{3 \sqrt{2} }{2}$