Question

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

Answer 1

$\huge\mathfrak\red{answer}$

$Given : \\ </p><p></p><p>x = 2 - \sqrt{3}x=2−3</p><p></p><p>$

$To \: find : \\ </p><p></p><p>(x - \frac{1}{x} ) {}^{3}(x−x1)3</p><p></p><p>$

$Solution :</p><p></p><p>$

$\begin{gathered}x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{(2) {}^{2} - ( \sqrt{3} ) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 + \sqrt{3} \end {gathered} \\ x=2−3x1=2−31×2+32+3x1 \\ =(2)2−(3)22+3x1=4−32+3x1=2+3</p><p></p><p>$

$Now, \\ </p><p></p><p>\begin{gathered}x - \frac{1}{x} = \\ 2 - \sqrt{3} - 2 - \sqrt{3} \\ \\ x - \frac{1}{x} = - 2\sqrt{3} \end{gathered}x−x1=2−3−2−3x−x1=−23</p><p></p><p>$

$And,</p><p></p><p>\begin{gathered}(x - \frac{1}{x} ) {}^{3} \\ \\ - (2 \sqrt{3} ) {}^{3} \\ \\ \therefore \boxed {\bold{- 24 \sqrt{3}}}\end{gathered}(x−x1)3−(23)3∴−243</p><p>$

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