1999年河南省高中数学竞赛有这样一道不等式试题:设x1,x2,y1,y2∈R*,a=x1x2+y1y2,b=(x1+x2)(y1+y2),试判断a,b的大小.不难证得结论为b≥a.本文给出这一不等式的推广,然后举例说明其应用.1推广及推论命题设aij0(i=1,2,…,m;j=1,2,…n),则(∑mi=1ai1∑mi=1ai2…∑mi=1ain)1n≥∑ 1999 Henan Province High School Math contest has such an inequality problem: Let x1, x2, y1, y2∈R *, a = x1x2 + y1y2, b = (x1 + x2) (y1 + y2), try to judge a, b Size is not difficult to prove that the conclusion is b ≥ a. This article gives the promotion of this inequality, and then gives an example of its application. 1 Generalization and inference proposition Let aij0 (i = 1,2, ..., m; j = 1,2 , ... n), then (Σmi = 1ai1Σmi = 1ai2 ... Σmi = 1ain) 1n≥Σ