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Combination

If x=2+21/3...

Question

If $x = 2 + 2^{\frac{1}{3}} + 2^{\frac{2}{3}}$ , then $x^{3} - 6 x^{2} + 6 x =$ ?

A

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B

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C

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D

3

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Solution

The correct option is A $2$
We have, $x = 2 + 2^{1 / 3} + 2^{2 / 3}$

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

$\Rightarrow (x - 2)^{3} = 2 + 4 + {3.2}^{1 / 3} {.2}^{2 / 3} (2^{1 / 3} + 2^{2 / 3})$

$\Rightarrow x^{3} - 8 - 6 x^{2} + 12 x = 6 + 6 (x - 2) [f r o m (1)]$

$\Rightarrow x^{3} - 6 x^{2} + 12 x - 8 = 6 + 6 x - 12$

$\Rightarrow x^{3} - 6 x^{2} + 6 x = 8 + 6 - 12 = 2$

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

Therefore, option $A$ is correct.

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Similar questions

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

x = 2 + 2^{\frac{1}{3}} + 2^{\frac{2}{3}}

, then the values of

x^{3} - 6 x^{2} + 6 x =

x = 2 + 2^{1 / 3} + 2^{2 / 3}

x^{3} - 6 x^{2} + 6 x - 2

x = 2 + 2^{2 / 3} + 2^{1 / 3},

then the value of

x^{3} - 6 x^{2} + 6 x

x = 2 + 2^{1 / 3} + 2^{2 / 3}

x^{3} - 6 x^{2} + 6 x =

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