将基本不等式a~2+b~2≥2ab(当且仅当a= b时等号成立)的两边加上a~2+b~2得:2(a~2+ b~2)≥(a+b)~2,即(a~2+b~2)/2≥((a+b)/2)~2,当且仅当a =b时等号成立.不等式(a~2+b~2)/2≥((a+b)/2)~2的左边为两个实数的平方的平均值,右边为此两个实数的平均值的平方.因而,我们称此不等式为 Add a ~ 2 + b ~ 2 to both sides of basic inequalities a ~ 2 + b ~ 2≥2ab (if and only if a = b holds): 2 (a ~ 2 + b ~ 2) ≥ (a + b) / 2 ≥ ((a + b) / 2) ~ 2 if and only if a = The left side of b ~ 2) / 2 ≥ ((a + b) / 2) ~ 2 is the average of the squares of two real numbers and the right side is the square of the average of two real numbers. Thus, we call this inequality