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

Question

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

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Answer

b
(b) $x = 2 + {2^{2/3}} + {2^{1/3}}\,\,\,\, \Rightarrow x - 2 = {2^{2/3}} + {2^{1/3}}$

Cubing both sides, we get

${x^3} - 8 - 6{x^2} + 12x = 6 + 6(x - 2)$

==> ${x^3} - 6{x^2} + 6x = 2$.

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