Quote by TenaliRaman
hmm..
well since a,b and c are all nonnegative and x,y,z are also nonnegative
Therefore set y,z to zero and keep incrementing x. The sum will always be increasing.
(Infact fix any two of (x,y,z) to any nonnegative value and keep on incrementing the third variable, as long as the coefficient of this third variable isnt zero).
 AI
P.S > Am i missing something?

Yes my fault terribly sorry. a, b, c are positive rational numbers, and x, y, z are positive integers, so yea nothing can be zero in my problem. I wasn't given this problem I created it and I am using it to solve another larger problem so sorry for the mistakes. Thank you for reading and trying to help.