If x+y+z=0, show that x3+y3+z3= 3xyz.
Solution and Explanation
It is known that,
\(\overline{x^3 + y^3 + z^3 - 3xyz} =\overline{ (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)}\)
put x + y + z = 0,
x3 + y3 + z3 - 3xyz = (0) (x2 + y2 + z2 - xy - yz - zx)
= x3 + y3 + z3 - 3xyz = 0
= x3 + y3 + z3 = 3xyz
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