Question

if x=1-under root 2 find ( x -i/x)^3​

Answer 1

i hope this will help you.

Answer 2

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

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

$\rm{rationalise \: the \: denominator}$

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

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

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

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

$\rm{now \:x - \frac{1}{x} = 1 - \sqrt{2} -[ - 1 + \sqrt{2} }]$

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

$\rm{\:x - \frac{1}{x} = 2 }$

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

$\fbox{\rm{{(\:x - \frac{1}{x} )}^{3} = 8 }}$