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26 August, 10:20

If x+y+z=0 show that

x+y+z=3xyz

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Answers (1)
  1. 26 August, 11:07
    0
    Step-by-step explanation:

    perhaps you mean

    x^3+y^3+z^3 = 3xyz

    because

    x+y+z = 0

    x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz - xz)

    (this equation is an identity)

    x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz - xz)

    x^3 + y^3 + z^3 - 3xyz = (0) (x^2 + y^2 + z^2 - xy - yz - xz)

    x^3 + y^3 + z^3 - 3xyz = 0

    x^3 + y^3 + z^3 = 3xyz
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