Question

x+y+z=0 then show that x3+y3+z3=3xyz

Answer 1

x + y + z = 0
Cube it on both the sides.
(x + y + z)^3 = 0^3
x^3 + y^3 + z^3 - 3xyz = 0
x^3 + y^3 + z^3 = 3xyz
Hence Proved.


[Thank You]

Answer 2

Solution :

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Given :

x + y + z = 0

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To Prove :

x³ + y³ + z³ = 3xyz

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Proof :

We know the identity that,

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx )

As x + y + z = 0,.

We get,.


⇒ x³ + y³ + z³ - 3xyz = (0)(x² + y² + z² - xy - yz - zx)

⇒ x³ + y³ + z³ - 3xyz = 0

⇒ x³ + y³ + z³ = 3xyz,.

                                     Hence proved,.

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                                           Hope it Helps !!