Question

if x =√2-1,then find the value of 1-1/x​

Answer 1

Answer:

Hope it is useful for all..

Answer 2

Answer:

$x = \sqrt{2} - 1$

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

$= \frac{ \sqrt{2} - 1 - 1}{ \sqrt{2} - 1}$

$= \frac{ \sqrt{2} - 2}{ \sqrt{2} - 1 }$

Rationalising the denominator we get:-

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

We use (a-b)(a+b) = a^2-b^2

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

$= - \sqrt{2}$