Question

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$if \: x = 2 - 2 \frac{1}{3}then \: value \: of \: x {3} - 6 {x}^{2} + 18x + 18 =$

Answer 1

$x =2-2^{1/3} \\ x - 2 = -{2}^{ \frac{1}{3} }$
take cube both sides,
$(x-2)^3=-2^{\frac{1}{3}\times3} \\ \\ {(x - 2) }^{3} = -2 \\ \\ {x}^{3} - 3 {x}^{2} 2 + 3x {2}^{2} - {2}^{3} = -2 \\ \\ {x}^{3} - 6 {x}^{2} + 12x - 8 = -2$
x³ - 6x² + 12x = 8 - 2 = 6
x³ - 6x² + 12x + 18 = 6 + 18 = 24

you did small mistake in typing ,
here, coefficient of x will be 12 .

then, answer should be 24