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Consistency of Linear System of Equations

If x= 2+223...

Question

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

1

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D

None of these

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Solution

The correct option is C $2$
Given $x - 2 = 2^{\frac{1}{3}} + 2^{\frac{1}{3}} .$ Cube both sides
${(x - 2)}^{3} = 2^{2} + 2 + {3.2}^{\frac{2}{3}} {.2}^{\frac{1}{3}} (x - 2)$
$(x - 2)^{3} = 6 + 6 (x - 2)$
$x^{3} - 6 x^{2} + 12 x - 8 = - 6 + 6 x$
$∴ x^{3} - 6 x^{2} + 6 x = 2$

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Similar questions

x = 2 + 2^{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^{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

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Consistency of Linear System of Equations

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