Question

question is x - 1 - V2.find (x-1/x)^3​ ​

Answer 1

Answer:

$\Large{\underline{\underline{\bf{RiGHt QuEsTiOn:-}}}}$

If x = 1 - √2,Find the value of (x-1/x)³

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$\sf \: x = 1 - \sqrt{2}$

$\longrightarrow \: \sf \dfrac{1}{x} \: = \dfrac{1}{1 - \sqrt{2} }$

Rationalize the denominator :

$\longrightarrow \: \sf \dfrac{1}{x} \: = \dfrac{1 \times 1 + \sqrt{2} }{(1 - \sqrt{2})(1 + \sqrt{2} ) }$

$\longrightarrow \: \sf \dfrac{1}{x} \: = \dfrac{1 + \sqrt{2} }{( {1)}^{2} - (\sqrt{ {2})^{2} } }$

$\longrightarrow \sf \dfrac{1}{x} \: = \dfrac{1 + \sqrt{2} }{1 - 2 }$

$\longrightarrow \sf \dfrac{1}{x} \: = \dfrac{1 + \sqrt{2} }{ -1 }$

$\longrightarrow \: \sf \dfrac{1}{x} \: = - 1 - \sqrt{2}$

Put the value of x and 1/x :

$\bigstar \boxed{\sf \: (x - \frac{1}{x} ) ^{3} }$

$\longrightarrow \: \sf [(1 - \sqrt{2}) - ( - 1 - \sqrt{2} )] ^{3}$

$\longrightarrow \: \sf (1 - \sqrt{2} + 1 + \sqrt{2} ) ^{3}$

$\longrightarrow \: \sf (2) ^{3}$

$\longrightarrow \red{\sf \: 8}$

Hope it helps uhh

Answer 2

Answer:

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