Question

please
full solution

Answer 1

Answer:

,

x+y+z=0

x+y=−z(1)

Cubing both sides,

x3+y3+3xy(x+y)=−z3

From (1),

x3+y3+3xy(−z)=−z3

x3+y3+z3=3xyz

Now, dividing both sides by xyz ,

x3xyz+y3xyz+z3xyz=3

x2yz+y2xz+z2xy=3nation:

Answer 2

Given, x3 + y3 + z3 = 3xyz

Therefore, x3 + y3 + z3 - 3xyz =0

This means,

x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

Now if x + y + z = 0, then......

x3 + y3 + z3 - 3xyz = ( 0 ) (x2 + y2 + z2 - xy - yz - zx)  . . . . . . .... ..... ... .. . . .. . .....    [ subsituting the value of x + y + z ]

x3 + y3 + z3 - 3xyz = 0   

x3 + y3 + z3 = 3xyz .  

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