Question

if x+y+z=0 show thatx^3+y^3+z^3=3xyz
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Answer 1

Step-by-step explanation:

we know that :-

x'3 + y'3 + z'3 - 3xyz = ( x+y+z ) ( x'2 + y'2 + z'2 - xy - yz - zx )

putting the value of x+y+z =0

x'3 + y'3 + z'3 - 3xyz = (0) ( x'2 + y'2 + z'2 - xy - yz - zx )

x'3 + y'3 + z'3 - 3xyz = 0

x'3 + y'3 + z'3 = 3xyz

hence proved...

hope it will help you