Question

在横线上填写恰当的符号(＞，＜，≥，≤).

若a、b、c是不全相等的正数，那么(a+b)(b+c)(c+a)_________8abc；a+b+c_________.

Answer 1

解析：a＋b≥2＞0，                                                                                                     ①

b＋c≥2＞0，                                                                                                                ②

c＋a≥2＞0.                                                                                                                  ③

∵a、b、c是不全相等的正数，∴①②③中的等号不能同时成立.

∴(a+b)(b+c)(c+a)＞8abc.

∵a＋b≥2，                                                                                                                 ①

b＋c≥2，                                                                                                                     ②

c＋a≥2.                                                                                                                              ③

这三个式子不能同时取等号，相加后得a+b+c＞.

答案：＞  ＞