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18 March, 13:56

X+y+z=0

x^2+y^2+z^2=1

x^4+y^4+z^4=?

+2
Answers (1)
  1. 18 March, 15:57
    0
    x^4+y^4+z^4 = 0.5 is the answer.

    Step-by-step explanation:

    we know that given,

    x+y+z=0

    x^2+y^2+z^2=1

    x^4+y^4+z^4=?

    ∴ 2 (xy+yz+zx) = (x+y+z) ^2 - (x^2+y^2+z^2) = - 1

    (xy + yz + zx) = - 1 : 2

    We also know the formula,

    6xyz = (x+y+z) ^3 - 3 (x+y+z) (x^2+y^2+z^2) + 2 (x^3+y^3+z^3) = 1

    xyz = 1 : 6

    x^4+y^4+z^4 = (x^2+y^2+z^2) ^2 - 2 (x^2y^2+y^2z^2+z^2x^2)

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

    = 1 - 2 (1:4) - 2 (1:6) (0)

    = 0.5
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