STARS wrote: Let a, b, c be positive integers. Prove that the inequality \[ (x - y)^a(x - z)^b(y - z)^c \ge 0 \] holds for all reals x, y, z if and only if a, b, c are even. Are U sure your problem true?I don't think it allways true for all reals x, y, z and a, b, c be positive integers

onlylove_math wrote: STARS wrote: Let a, b, c be positive integers. Prove that the inequality \[ (x - y)^a(x - z)^b(y - z)^c \ge 0 \] holds for all reals x, y, z if and only if a, b, c are even. Are U sure your problem true?I don't think it allways true for all reals x, y, z and a, b, c be positive integers Oh my friend,i think you didint understand the question " "holds for all reals x, y, z if and only if a, b, c are even." If a, b, c are even."the proof is very easy But the first case is hard I only have some ideals :Let$ x=0,y>0,z<0$ and check $ a,b,c$ But i cant finish it .sorry