Question

已知a b c为三个不相等的正数,且abc=1.求(1+a+b)(1+b+c)(1+c+a)大于27

Answer 1

左边≥3(1*a*b)^(1/3)*3(1*b*c)^(1/3)*3(1*c*a)^(1/3) =27(a^2b^2c^2)^(1/3) =27[(abc)^2]^(1/3) =27*1 =27 得证