Question

if x = 1-root2 find the value of (x - 1/x)^3.


PLEASE DO IT ITS URGENT
IF U WILL DO IT I WILL MARK U AS BRAINLIST

Answer 1

hey dear
hope it helps u

Answer 2

Given x = 1 - root2.

Now,


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

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

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

                        $= -1 - \sqrt{2}$



Now,

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

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

         $= 1 + 1$

         = 2.


Therefore:

$(x - \frac{1}{x} )^3 = (2)^3$

         = 8




Hope this helps!