Question

under what condition x3+y3+z3=3xyz​

Answer 1

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

So when x+y+z=0,

x³+y³+z³-3xyz=0

x³+y³+z³=3xyz

Therefore,

x³+y³+z³=3xyz if x+y+z=0

Answer 2

Answer:

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Explanation:

Solution : We know that x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx). If x + y + z = 0, then x3 + y3 + z3 – 3xyz = 0 or x3 + y3 + z3 = 3xyz.