Question

Please find the answer of this question . The circled one

Answer 1

$x = \frac{ \sqrt{3} }{2} \\ we \: have \: to \: find \: {x}^{3} + \frac{1}{ {x}^{3} } = (x + \frac{1}{x} ) ^{3} - 3x - \frac{3}{x}$

Plug-in the value of x and simply it .

$= ( \frac{{ \sqrt{3} } }{2} + \frac{1}{ \frac{ \sqrt{3} }{2} } )^{3} - \frac{ 3\sqrt{3} }{2} - \frac{6}{ \sqrt{3} } \\ = ( \frac{ \sqrt{3} }{2} + \frac{2}{ \sqrt{3} } ) ^{3} - ( \frac{9 + 12}{2 \sqrt{3} } ) \\ = (\frac{7}{2 \sqrt{3} }) ^{3} - \frac{21}{2 \sqrt{3} } \\ = \frac{343}{24 \sqrt{3} } - \frac{21}{2 \sqrt{3} } \\ = \frac{343 - 252}{24 \sqrt{3} } = > \frac{91 }{24 \sqrt{3} }$

Multiply and divide by √3
=> (91√3)/72
Hence Option (b) is correct !

Answer 2

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