If x = 2^{1/3} - 2^{-1/3},find the value of 2 | vedclass

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(C) Given $x = 2^{1/3} - 2^{-1/3}$.We need to find the value of $2x^3 + 6x$.First,cube both sides of the equation $x = 2^{1/3} - 2^{-1/3}$:$x^3 = (2^{

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$3$

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(C) Given $x = 2^{1/3} - 2^{-1/3}$.We need to find the value of $2x^3 + 6x$.First,cube both sides of the equation $x = 2^{1/3} - 2^{-1/3}$:$x^3 = (2^{1/3} - 2^{-1/3})^3$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 the terms:$2x^3 + 6x = 3$.

If $x = 2^{1/3} - 2^{-1/3}$,find the value of $2x^3 + 6x$.

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