“如果a ,b∈R ,那么a2 +b2 ≥2ab(当且仅当a =b时取“=”号)”,这是高中数学一个非常重要的定理,有着广泛的应用.如果限定a ,b∈R+ ,则得到a +b2 ≥ab ,其中a +b2 、ab分别称为正数a、b的算术平均数与几何平均数.对此,《教师教学用书》要求:“掌握两个(不扩展到三个)正数的算 “If a, b∈R, then a2 + b2 ≥ 2ab (when and only if a = b = ”sign"), which is a very important theorem of high school mathematics, has a wide range of applications. If you limit a, b∈R+, then get a +b2 ≥ab, where a +b2, ab are respectively called the arithmetic mean and the geometric mean of the positive numbers a, b. For this, the “teacher’s teaching book” requires: “Master two ( Does not extend to three) positive numbers