Given, cube root a + cube root b + cube root c = 0
so, a^1/3 + b^1/3 = - c^1/3
=> (a^1/3 + b^1/3)^3 = (- c^1/3)^3
=> a + b + 3(a^1/3)(b^1/3)(a^1/3 + b^1/3) = - c
=> a + b + 3(a^1/3)(b^1/3)(- c^1/3) = - c
=> a + b - 3(a^1/3)(b^1/3)( c^1/3) = - c
=> a + b + c = 3(a^1/3)(b^1/3)( c^1/3)
=> (a + b + c)^3 = {3(a^1/3)(b^1/3)( c^1/3)}^3
=> (a + b + c)^3 = 27abc
HENCE PROVED ........................
