本文的例1至例4分别是文[1]的例1至例4,文[1]对这类轮换对称不等式的证明的方法是先猜想不等式等号成立的条件是a=b=c,然后利用基本不等式进行构造证明,方法巧妙,但操作较为麻烦,笔者发现这类不等式用柯西不等式的变式很容易证明.下面对这4道例题用柯西不等式的变式给 Examples 1 to 4 of this paper are examples 1 to 4 of [1], respectively. The proof of this kind of rotation symmetric inequality is that [1] suppose that the inequality equals sign a = b = c, And then use the basic inequality to prove the structure, the method is clever, but the operation is more troublesome, I found that such inequalities Cauchy inequality is easy to prove the following four examples of Cauchy inequality of variation