Question

[Hậu Duệ Mặt Trời]

giai,cho,minh,bai,nay,di cho,a,b,c>=0.CMR:a^3+b^3+c^3>=3abc

Answer 1

[Nguyễn Minh Khang]

a+b+c=0
a+b=-c
(a+b)^3=(-c)^3
a^3+3a^2b+3ab^2+b^3=(-c)^3
a^3+b^3+c^3=-3a^2b-3ab^2
a^3+b^3+c^3=-3ab(-c)
a^3+b^3+c^3=3abc