Question

Give the right answer.
$x = \sqrt[3]{2 + \sqrt{3} } \: \: then \: find \: x {}^{3} + \frac{1}{ {x}^{3} }$
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Answer 1

x^3 = 2+root3
=> 1/x^3 = 1/(2+root3) = 2-root3 (by rationalisation)
x^3+(1/x^3) = 2 + root3 + 2 - roog3 = 4