普通高中课程标准实验教科书《数学》选修《不等式选讲》中介绍了一个非常优美的不等式———柯西不等式,各种形式的柯西不等式是许多现代数学理论的出发点,在数学的很多分支中有着广泛的应用.定理(柯西不等式的代数形式)设a1,a2,b1,b2均为实数,则(a1b1+a2b2)2≤(a21+a22)(b21+ A very graceful inequality, Cauchy’s inequality, is introduced in the textbook “Mathematical Elective”, which is an experimental textbook for the general high school curriculum. The various forms of Cauchy’s inequality are the starting points for many modern mathematical theories. In many branches of mathematics (A1b1 + a2b2) 2≤ (a21 + a22) (b21 + a22) is a real number, the theorem (Cauchy inequality algebraic form)