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

Answer

2

Explanation

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`