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Integration of Piecewise Continuous Functions

If x= 2+22/...

Question

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

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Solution

Given $x - 2 = 2^{1 / 3} + 2^{1 / 3} .$ Cube both sides
${(x - 2)}^{3} = 2^{2} + 2 + {3.2}^{2 / 3} {.2}^{1 / 3} (x - 2)$
$= 6 + 6 (x - 2)$
or $x^{3} - 6 x^{2} + 12 x - 8 = - 6 + 6 x .$
$∴ x^{3} - 6 x^{2} + 6 x = 2.$

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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^{\frac{2}{3}}

2^{\frac{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 =

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

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