Question

If x= 1+√2 then find the value of (x-1/x)^3​

Answer 1

Step-by-step explanation:

see the attachement...

Answer 2

Answer:

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

by rationalising denominator we get,

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

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