Question

if one upon x is equal to root 2 + 1 find x + 1 upon x
$1 \ \div x = root2 + 1 find x + 1 \div x$
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Answer 1

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

Now,

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