Question

x+y+z=0 prove that x³+y³+z³=3xyz.​

Answer 1

Answer:

given

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

Step-by-step explanation:

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

hence

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

proved