Question

If x = 1 - √2 , find the value of x+1/x​

Answer 1

$x = 1 - \sqrt{2}$

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