柯西不等式:设a1,a2,…,an,b1,b2,…,bn∈R,则(a12+a22+…+an2)(b12+b22+…+bn2)≥(a1b1+a2b2+…+anbn)2.当且仅当bi=0(i=1,2,…,n)或存在数k,使得ai=kbi(i=1,2,…,n)时,等号成立。柯西不等式形式优美,具有重大的应用价值,并且作为新增内容进入新课程的选修教材《不等式选讲》。浙江省普通高中新课程实验数学学科教学指导意见对柯西不等式考查的要求为:“认识柯西不等式 Cauchy inequality: (a12 + a22 + ... + an2) (b12 + b22 + ... + bn2) ≥ (a1b1 + a2b2 + ... + anbn) 2 if a1, a2, ..., an, b1, b2, Equal sign is true if and only if bi = 0 (i = 1, 2, ..., n) or there is a number k such that ai = kbi (i = 1,2, ..., n). Cauchy inequality has the form of a beautiful, has great application value, and as an added content into the new course optional textbook ”inequality election stresses.“ Zhejiang General High School New Curriculum Experimental Mathematics Subject Teaching Guidance The test of Cauchy’s inequality requires: ”Understanding Cauchy’s inequality