Question

if x=1-√2 find the value of (x-1/x)4​

Answer 1

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Given:-

• x = 1-√2

Solution:-

$\sf \: x = 1 - \sqrt{2} \\ \\ \therefore \sf \: x - \frac{1}{x} = (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \times \frac{(1 + \sqrt{2}) }{(1 + \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{(1 + \sqrt{2} )}{ {(1)}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \sf \implies \: 1 - \sqrt{2} - \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \sf \implies \: (1 - \sqrt{2} ) - ( - 1 + \sqrt{2} ) \\ \\ \sf \implies \: 1 - \sqrt{2} + 1 + \sqrt{2} \\ \\ \sf \implies \: 1 + 1 \\ \\ \sf \implies \: 2 \\ \\ \sf \therefore \: { \left(x - \frac{1}{x}\right ) }^{4} = {(2)}^{4} = 16$

Answer 2

Answer:

\huge{ \underline{ \underline{ \mathscr{ \red{Answer : }}}}}

Answer:

Given:-

x = 1-√2

Solution:-

\begin{gathered}\sf \: x = 1 - \sqrt{2} \\ \\ \therefore \sf \: x - \frac{1}{x} = (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \times \frac{(1 + \sqrt{2}) }{(1 + \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{(1 + \sqrt{2} )}{ {(1)}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \sf \implies \: 1 - \sqrt{2} - \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \sf \implies \: (1 - \sqrt{2} ) - ( - 1 + \sqrt{2} ) \\ \\ \sf \implies \: 1 - \sqrt{2} + 1 + \sqrt{2} \\ \\ \sf \implies \: 1 + 1 \\ \\ \sf \implies \: 2 \\ \\ \sf \therefore \: { (x - \frac{1}{x} ) }^{4} = {(2)}^{4} = 16\end{gathered}

x=1−

2

∴x−

x

1

=(1−

2

)−

(1−

2

)

1

⟹(1−

2

)−

(1−

2

)

1

×

(1+

2

)

(1+

2

)

⟹(1−

2

)−

(1)

2

−(

2

)

2

(1+

2

)

⟹1−

2

−

1−2

1+

2

⟹(1−

2

)−(−1+

2

)

⟹1−

2

+1+

2

⟹1+1

⟹2

∴(x−

x

1

)

4

=(2)

4

=16