Question

a, b, c are distinct non-zero reals such that (1 + a³)/a = (1 + b³)/b = (1 + c³)/c. Find all possible values of a³ + b³ + c³.

Answer 1

Alternate

abc = – 1.

a³ + b³ + c³ = (a + b + c) (a² + b² + c² – ab – bc – ca) + 3abc

= (0) (a² + b² + c² – ab – bc – ca) + 3(– 1) = 0 – 3 = – 3.