The Application Of Cauchy Inequality N Senior High Mathematics

Cauchy Inequality is very useful in many areas, especially in the Proof ofinequalities, equations, function the most value and the range of variables, geometryand other aspects． Flexible and ingenious application of it can make some of themore difficult problems to be solved．Since the21st, the new-curriculum has greatly reformed． In2003, the ministry ofEducation issued “The Common Senior High School Mathematics standards(experiment)”． In2008, all the schools of every province of china used the“Standard" for teaching． Under the ideas of spreading the new curriculum standards,Elective4-5topics—Inequalities Selected Topics were selected into thecurriculums． As an elective content, Cauchy inequality can not only expand thestudents’ knowledge, but also enhance students’ imagination． Meanwhile, it alsobrings a new challenge for educators．After checking some relevant documents, I find that the applications of the CauchyInequality in middle school mathematics curriculum not only emphasize the study ofsolutions, but also lack of discovery of the educational value and systematicresearch． Now in this article, firstly, the different manifestations of CauchyInequality are given． Secondly, by different methods, the Cauchy Inequality isproved． Thirdly, the educational value of the Cauchy Inequality contained in thenew curriculum is discussed． Lastly, by collecting the questions of the collegeentrance examination and competitions which related to the Cauchy Inequality, andanalyzing the characteristics of those questions, some applications of CauchyInequality are given．...