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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:

Text Solution

Verified by Experts

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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Knowledge Check

  • If x = 2^(1//3) + 2^(-1//3) then the value of 2x^3 - 6x will be :

    A
    5
    B
    `-5`
    C
    `1`
    D
    `0`

  • If x=2^(1//3)+2^(-1//3) then the value of 2x^3-6x will be :

    A
    5
    B
    -5
    C
    1
    D
    0

  • If x=2^(1//3)-2^(-1//3) then what is the value of 2x^(3)+6x ?

    A
    1
    B
    2
    C
    3
    D
    4

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