Question

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

Answer 1

Step-by-step explanation:

x=√2+1

1/x=√2-1/(√2-1)(√2+1)=√2-1/2-1=√2-1

x-1/x=√2+1-√2+1=2

(x-1/x)^3=2^3=8

Answer 2

$\huge\mathcal\red{Solution}$

${x - \binom{1}{3}^{3} = 8}$

$\huge\mathcal\red{Given:-}$

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

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

$\implies{\frac{1+ \sqrt{2}}{1² - (\sqrt{2}^2)}}$

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

$\implies{-(1 + \sqrt{2})}$

$\huge\mathcal\red{Now}$

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

$\implies{((1- \sqrt{2} - {-((1+ \sqrt{2}))}}^{3}$

$\implies{(1 - \sqrt{2} + 1 + \sqrt{2})}^{3}$

$\implies{2}^{3}$

$\implies{8}$