Question

if x+y+z=0 then what is x³+y³+z³+3xyz​

Answer 1

If x+y+z=0,

Then

x³+y³+z³-3xyz​ = 0 or we can say that x³+y³+z³=3xyz

PROOF:-

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

hence

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

PLZ MARK AS BRAINLIEST

Answer 2

x+ y + z= 0

x+ y= - z

Cubing both sides we get

x3 +y3+ 3xy(x+y)= -z3

x3+ y3+z3= 3xyz(Putting value of x+ y as -z )

Adding 3xyz on both sides we get

x3+ y3+ z3 + 3xyz = 6 xyz