Question

X + Y + Z is equals to zero then show that x cube + y cube + Z cube equals to 3 x y z​

Answer 1

It may be right answer and hope it helps you.

Answer 2

Answer:

there is an identity

(a×a×a)+(b×b×b)+(c×c×c)-3abc=(a+b+c)(a×a+b×b+c×c-ab-bc-ca

and if a+b+c = 0

then

(a×a×a)+(b×b×b)+(c×c×c)-3abc =( 0)(a×a+b×b+c×c-ab-bc-ca

(a×a×a)+ (b×b×b)+(c×c×c)-3abc =0

(a×a×a)+(b×b×b)+(c×c×c)=3abc

hence proved