Question

if x=2-√3, find the value of (x-1/x) of power 3

Answer 1

x=2-√3
=>1/x = 1/(2-√3)
=>1/x=2+√3
Now,
x-(1/x)=(2-√3)-(2+√3)
=>x-(1/x)=-2√3
=>{x-(1/x)} ³=-24√3

Answer 2

Hey mate!

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Given :

$x = 2 - \sqrt{3}$

To find :

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

Solution :

$x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{(2) {}^{2} - ( \sqrt{3} ) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 + \sqrt{3}$

Now,

$x - \frac{1}{x} = 2 - \sqrt{3} - 2 - \sqrt{3} \\ \\ x - \frac{1}{x} = - 2\sqrt{3}$

And,

$(x - \frac{1}{x} ) {}^{3} \\ \\ - (2 \sqrt{3} ) {}^{3} \\ \\ \therefore \boxed {\bold{- 24 \sqrt{3}}}$

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Thanks for the question !

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