柯西不等式的证明及应用

Proof of Cauchy-inequality and Its Application

给出经典柯西不等式的几种证明方法,以及在其他数学分支中的推广形式.利用这些推广形式推导和证明了中学数学和其他数学分支中的一些重要公式,揭示了柯西不等式应用的广泛性.

In this paper,we first introduces the classic form of the Cauchy inequality and gives its several proving methods,then discusses its four generalization forms in various fields of mathematics.Using these generalization forms,some important formula in secondary school mathematics and other branches of mathematics fields are derived and proved,revealing the wide applications of the Cauchy-inequality.