(C) Given $x = 2^{1/3} - 2^{-1/3}$.Cube both sides: $x^3 = (2^{1/3} - 2^{-1/3})^3$.Using the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$:$x^3 = (2^{

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(C) Given $x = 2^{1/3} - 2^{-1/3}$.Cube both sides: $x^3 = (2^{1/3} - 2^{-1/3})^3$.Using the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$:$x^3 = (2^{1/3})^3 - (2^{-1/3})^3 - 3(2^{1/3})(2^{-1/3})(2^{1/3} - 2^{-1/3})$.$x^3 = 2 - 2^{-1} - 3(1)(x)$.$x^3 = 2 - 1/2 - 3x$.$x^3 = 3/2 - 3x$.Multiply by $2$: $2x^3 = 3 - 6x$.Rearranging gives: $2x^3 + 6x = 3$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

A
$1$
B
$2$
C
$3$
D
None of these

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If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

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