1. The problem statement, all variables and given/known data Let a,b,c be distinct real numbers satisfying [itex]a^3+b^3+6abc = 8c^3 [/itex] then which of the following may be correct? A) a,c,b are in Arithmetic Progression B) a,c,b are in Harmonic Progression C) a+bω-2cω^2 =0 D) a+bω^2-2cω=0 3. The attempt at a solution I could prove the first statement but I really can't figure out how to deal with the other options. Since the first statement is correct all I know is that 2c=a+b. Suppose I replace a with 2c-b in the third statement and simplify it, I get 4c-b+ω(2c+b) = 0. But I guess LHS can't be zero(I'm not sure about this).