(a+b)(b+c)(c+a)=(a+b+c-a)(a+b+c-b)(a+b+c-c)=(a+b+c)(ab+ac+bc)-abc
9(a+b+c)(ab+ac+bc)-9abc-8(ab+bc+ca)(a+b+c)=(a+b+c)(ab+ac+bc)-9abc
a+b+c≧3(abc)^(1/3)
ab+ac+bc≧3(abc)^(2/3)
(a+b+c)(ab+ac+bc)≧9abc