Question

if x= 1+under root 2 then find the value of (x-1/x)raised to power 3​

Answer 1

Step-by-step explanation:

x=1+√2

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

rationalising the denominator

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

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

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

$= \sqrt{2} - 1$

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

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

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