来自恒东辉的问题
(选修4-5:不等式选讲)已知正数a,b,c满足abc=1,求证:(a+2)(b+2)(c+2)≥27.
(选修4-5:不等式选讲)
已知正数a,b,c满足abc=1,求证:(a+2)(b+2)(c+2)≥27.


(选修4-5:不等式选讲)已知正数a,b,c满足abc=1,求证:(a+2)(b+2)(c+2)≥27.
(选修4-5:不等式选讲)
已知正数a,b,c满足abc=1,求证:(a+2)(b+2)(c+2)≥27.
证明:由于正数a,b,c满足abc=1,
故有(a+2)(b+2)(c+2)=(a+1+1)(b+1+1)(c+1+1)≥33a