Question

If x+y+z = 0, then x³ +y³ +z³ (a)0 = (b)-3xyz (c) xyz (d)3xy​

Answer 1

Answer:

Given x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y)  

3

=(−z)  

3

 

⟹x  

3

+y  

3

+3x  

2

y+3xy  

2

=−z  

3

 

⟹x  

3

+y  

3

+3xy(x+y)=−z  

3

 

⟹x  

3

+y  

3

+3xy(−z)=−z  

3

 

⟹x  

3

+y  

3

−3xyz=−z  

3

 ⟹x  

3

+y  

3

+z  

3

=3xyz

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given x+y+z=0

⟹x+y=−z

(a - b)3 = a3 - 3a2b + 3ab2 - b3