Question

if x= 1-√2 , find the value of (x - 1/x) ^3

Answer 1

Given:-

$x = 1 - \sqrt{2}$

To find :-

The value of

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

Solution:-

$(x - \frac{1}{x} )3 \\ = (1 - \sqrt{2} - \frac{1}{1 - \sqrt{2} } )^{3} \\ = ( \frac{ - 1 - 1}{1 - \sqrt{2} } )^{3} \\ = ( \frac{ - 2}{1 - \sqrt{2} } ) ^{3} \\ = \frac{ - 8}{7 - 3 \sqrt{2} - 2 \sqrt{2} } \\ = \frac{ - 8}{7 \sqrt{2} }$

Answer 2

Answer:

$given \: = x \: = 1 - \sqrt{2} \\ \\ solution \: = \\ \\ {(x \: - \frac{1}{x}) }^{3} \\ \\ {(1 - \sqrt{2} - \frac{1}{1 - \sqrt{2} } )}^{3} \\ \\ { (\frac{ - 1 - 1}{1 - \sqrt{2} }) }^{3} \\ \\ \frac{ - 8}{7 - 3\sqrt{2} - 2 \sqrt{2} } \\ \\ \frac{ - 8}{7 - 5 \sqrt{2} }$