题目

已知a,b,c是不全相等的正数,求证:a(b2+c2)+b(c2+a2)+c(a2+b2)＞6abc. 答案：证明:∵b2+c2≥2bc,a＞0,∴a(b2+c2)≥2abc.                               ①同理,b(a2+c2)≥2abc,                          ②c(a2+b2)≥2abc.                                  ③∵a,b,c不全相等,∴b2+c2≥2bc,c2+a2≥2ac,a2+b2≥2ab三式不能全取“=”，从而①②③三式也不Xi'an is one of _____ capital _____ in China. [     ]A. older; city B. the older; city C. oldest; cities D. the oldest; cities