if x+y+z = 0 , show that x^3+ y^3+ z^3 = 3xyz
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Given, x3 + y3 + z3 = 3xyz
Therefore, x3 + y3 + z3 - 3xyz =0
This means,
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
Now if x + y + z = 0, then......
x3 + y3 + z3 - 3xyz = ( 0 ) (x2 + y2 + z2 - xy - yz - zx) . . . . . . .... ..... ... .. . . .. . ..... [ subsituting the value of x + y + z ]
x3 + y3 + z3 - 3xyz = 0
x3 + y3 + z3 = 3xyz .
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