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Higher Order Equations

If x= 2+ 22/3...

Question

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

A

3

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B

2

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C

- 3

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D

- 2

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Solution

The correct option is B $2$
Given:
$x = 2 + 2^{2 / 3} + 2^{1 / 3}$
$\Rightarrow x - 2 = 2^{2 / 3} + 2^{1 / 3},$
Cubing the equation on both sides, we get
$\Rightarrow (x - 2)^{3} = 4 + 2 + 3 \times 2^{2 / 3} \times 2^{1 / 3} (2^{2 / 3} + 2^{1 / 3})$
$\Rightarrow x^{3} - 8 + 6 x (x - 2) = 6 + 6 (x - 2)$
$\Rightarrow x^{3} - 6 x^{2} + 12 x - 8 = - 6 + 6 x$
$∴ x^{3} - 6 x^{2} + 6 x = 2$

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Similar questions

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

, then the value of

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

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 - 2

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

2^{\frac{1}{3}}

then the value of

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

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

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