Question

If x^1/3 + y^1/3 + z^1/3 = 0 ,
Then prove ( x+y+z)^3 = 27 xyz

Answer 1

Answer:

Step-by-step explanation:

consider LHS

given

x^(1/3)+y^(1/3)=(-z)^(1/3)

cubing on both sides

x+y+3(xy)^1/3(x^1/3+y^1/3)=-z

x+y+z-3(xy)^1/3(-z^1/3)=0

x+y+z=3(xyz)^1/3

cubing on both sides

(x+y+z)^3=27xyz=RHS