Question

if x=1-√2,find the value of [x-1/x]³​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• X=1-√2

${\sf{\green{\underline{\large{To\:find}}}}}$

• $\tt{(X-}\dfrac{1}{X})^3$

${\sf{\pink{\underline{\Large{Explanation}}}}}$

☞we know that( a+b)³

( a+b)³=a³+b³+3ab(a+b)

$\tt{(X-}\dfrac{1}{X})^3=x^3\dfrac{1}{x^3}+3\times\frac{1)(X}\times{(X+\frac{1}{X})}$

Now Rationalize 1/x

$\tt\dfrac{1}{x}=\dfrac{1}{1-\sqrt{2}}$

Now Rationalize

$\implies\tt\dfrac{1}{x}=\dfrac{1}{1-\sqrt{2}}\times\dfrac{1+\sqrt{2}}{1+\sqrt{2}}$

$\implies\tt\dfrac{1}{x}=\dfrac{1+\sqrt{2}}{-1}$

$\implies\tt\dfrac{1}{x}=\dfrac{-1-\sqrt{2}}{1}$

Now putting the values

(X+1/X)³=(+1-√2-1-√2)³

=(-√2)³

=-2√2