Question

if
$x = 1 + \sqrt{2}$
then the value of
$x + \frac{1}{x}$
will be?

*please explain step by step*​

Answer 1

$x = \sqrt{2} + 1 \\ x = ( \sqrt{2} + 1) \frac{( \sqrt{2} - 1) }{( \sqrt{2} - 1) } \\ x = \frac{1}{ \sqrt{2} - 1} \\ \frac{1}{x} = \sqrt{2} - 1\\now\\x+\frac {1}{x}=\sqrt {2}+1+\sqrt {2}-1 \\=2\sqrt {2}$

hope it helps