Question

if x + y + z = to 0 then x³ + y³ + z³ is equal to​

Answer 1

Answer:

3xyz

Step-by-step explanation:

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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Answer 2

Answer:

3xyz

Step-by-step explanation:

Given

x+y+z=0. ------(1)

then

x+y= -z

Cubing on both side

(x+y)^3= -z^3

formula =(x+y)^3= x^3+3xy(x+y)+ y^3

so here also

x^3+3xy(x+y)+y^3 = -z^3

x^3+3xy( -z)+y^3= -z^3

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