No, you are wrong. You said, you can find numbers a,b,c which fulfil conditions for any x, but you must find x, which for any possible a,b,c (a+b+c=3) is filfuled. for example you said x=-50. it is wrong but I can find numbers a,b,c which isnt filfuled (a^3+b^3+c^3>=3).. for example a=-50 b=26 c=27