English, asked by prachi12345677, 11 months ago

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

Answers

Answered by Intelligentcat
80

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

Answered by anishakumari40
0

Answer:

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