Question

if x=1+√2 then find the value of (x-1/x)​

Answer 1

Given ,

• x = 1 + √2

Now,

$\large\bold \color{blue}{x - \frac{1}{x} }$

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

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

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

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

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

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

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

$= \bold {\boxed{2 \sqrt{2} }}$