Question

If x+y+z=0 then x^3+y^3+z^3-3xyz=?
Please step by step explain

Answer 1

Answer:

If x+y+z=0 then x³+y³+z³-3xyz=0

x³+y³+z³=3xyz

Step-by-step explanation:

Answer 2

Answer:

x^3 + y^3 + z^3 - 3xyz = 0

Step-by-step explanation:

Given, x^3 + y^3 + z^3 = 3xyz

Therefore, x^3 + y^3 + z^3 - 3xyz =0

This means,

x^3 + y^3 + z^3 - 3xyz = (x + y + z)•(x^2 + y^2 + z^2 - xy - yz - zx)

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

x^3 + y^3 + z^3 - 3xyz = ( 0 ) (x^2 + y^2 + z^2 - xy - yz - zx)  . . . . . . .... ..... ... .. . . .. . .....    [ subsituting the value of x + y + z ]

x^3 + y^3 + z^3 - 3xyz = 0   

x^3 + y^3 + z^3 = 3xyz .

=> x^3 + y^3 + z^3 - 3xyz = 0

Hence, proved.