If x + y + z = 0, then x3 + y3 + z3 is equal to :
A. 0
B. 3xyz
C. $$\frac{{{\text{xy}} + {\text{yz}} + {\text{zx}}}}{{{\text{xyz}}}}$$
D. xyz(xy + yz + zx)
Answer: Option B
Solution(By Examveda Team)
Given,
x + y + z = 0
Cubing both side,
(x + y + z)3 = 0
x3 + y3 + z3 - 3xyz = 0 [using formula]
x3 + y3 + z3 = 3xyz
This Question Belongs to Arithmetic Ability >> Number System
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Comments ( 3 )
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
Let x = 1; y = -2 and z = 1. Then x+y+z = 0, but x^3 + y^3 + z^3 = 10 and not 3xyz.
Someone correct me if I am wrong.
if x+y+z = 0 i.e. x=0, y=0, z=0
so answer would be 0 .