If x = 2^ 1/3 - 2^ - 1/3 , then 2 x^3 + 6x = - Vidyadip

Question

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

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Answer

c
(c) $x = {2^{1/3}} - {2^{ - 1/3}}$

$ \Rightarrow $${x^3} = 2 - {2^{ - 1}} - {3.2^{1/3}}{.2^{ - 1/3}}({2^{1/3}} - {2^{ - 1/3}})$

$ \Rightarrow $${x^3} = 2 - {1 \over 2} - 3x$ ==> ${x^3} + 3x = {3 \over 2}$

$\therefore 2{x^3} + 6x = 3$.

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