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有五种平均数 ,在应用中十分重要 ,它们之间有怎样的大小关系呢 ?我们可以用几何方法加以证明 .在 a0 ,b 0且 a≠ b时 ,不妨设 a b,我们可以通过以下两个几何模型比较五种中项 2 aba + b,ab,a + b2 ,a2 + b22 ,a2 + b2a + b 的大小关系 .1.如图 1,B为 AH上的点 ,且 AB =a,AH
There are five kinds of averages, which are very important in the application. What kind of size relationship between them? We can use geometric methods to prove. In a0, b0 and a≠b, we can set ab, we can pass the following two The geometric model compares the size relationships of the five middle terms 2 aba + b, ab, a + b2, a2 + b22, and a2 + b2a + b. 1. As shown in Figure 1, B is the point on AH, and AB = a, AH