Question

If x = 1-√2, the value of 1-1/x

Answer 1

Step-by-step explanation:

$given \: x = 1 - \sqrt{2} \: then \: \frac{1}{x} = \frac{1}{1 - \sqrt{2} } = \frac{1}{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } = \frac{1 + \sqrt{2} }{1 - 2} = \frac{1 + 2 + 2 \sqrt{2} }{ - 1} = \frac{ - 3 - 2 \sqrt{2} }{1} \\ now \: 1 - \frac{1}{x} =1 - ( - 3 - 2 \sqrt{2} ) = 1 + 3 + 2 \sqrt{2} = 4 + 2 \sqrt{2}$