pls answer this question.......
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AkshayAK123:
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if x + y + z = 0
then x ^ 3 + y ^ 3 + z ^ 3 = 3xyz
derivation..
( x^3+y ^3 + z ^3)- 3 xyz =( x+ y+ z)( x^2 + y ^2 + z^2 - xy - yz- zx )
( x ^3 + y^3 + z ^3) - 3 xyz = 0 ( since x + y + z = 0)
therefore , x^3 + y^3 + z ^3 = 3xyz..
hence, proved...
then x ^ 3 + y ^ 3 + z ^ 3 = 3xyz
derivation..
( x^3+y ^3 + z ^3)- 3 xyz =( x+ y+ z)( x^2 + y ^2 + z^2 - xy - yz- zx )
( x ^3 + y^3 + z ^3) - 3 xyz = 0 ( since x + y + z = 0)
therefore , x^3 + y^3 + z ^3 = 3xyz..
hence, proved...
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