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Factorisation Using Algebraic Identities

If x = 2 + ...

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

1

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C

2

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D

- 2

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Solution

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

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

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

$x^{3} - 8 - 6 x (x - 2) = 2 + 4 + {3.2}^{1 / 3 + 2 / 3} (2^{1 / 3} + 2^{2 / 3})$

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

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

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

$x^{3} - 6 x^{2} + 6 x = 14 - 12$

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

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Similar questions

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^{\frac{2}{3}}

2^{\frac{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 =

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