Question

If x=1+root2 then find the value of (x-1/x)​

Answer 1

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