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If x=2+2^(2/3)+2^(1/3), then the value o...

If `x=2+2^(2/3)+2^(1/3)`, then the value of `x^3-6x^2+6x` is:

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The correct Answer is:
2
Given `x-2=2^(2//3)+2^(1//3)`
Taking cube of both sides, we get
`(x-2)^(3)=2^(2)+2+3xx2^(2//3)xx2^(1//3)(x-2)`
`implies(x-2)^(3)=6+6(x-2)`
or `x^(3)-6x^(2)+12x-8=-6+6x`
`:.x^(3)-6x^(2)+6x=2`
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