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If x+y+z=0show that x^3+y^3+z^3=3x y z....

If `x+y+z=0`show that `x^3+y^3+z^3=3x y z`.

Answer

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Knowledge Check

  • If x = y + z then x^(3) - y^(3) - z^(3) is

    A
    0
    B
    3xyz
    C
    `-3xyz`
    D
    1

  • If x,y,z gt0, then (x^3+y^3+z^3)/(x^3y^3z^3)

    A
    `ge 1/x+1/y+1/z`
    B
    `le 1/x+1/y+1/z`
    C
    `ge x+y+z`
    D
    None of these

  • If x + y + z = 0 , then ( x + y - z)^(3) + ( y + z - x)^(3) + (z + x - y) ^(3) = k (xyz) , where k is equal to :

    A
    `-3`
    B
    `3`
    C
    `-24`
    D
    `9`

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    Solve the given equations: x +y +z=0 x^(3) + y^(3) +z^(3)=18 x^(7) + y^(7) + z^(7) = 2058 where x,y,z in R

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    x =y + z then x ^(3) - y ^(3) - z ^(3) is

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