1.知识具备x2≥0→(a-b)2≥0→a2+b2-2ab≥0,即:(1)a2+b2≥2ab,注意乘积为定值,平方和有最小值,当且仅当a=b时取等号.(2)ab≤a2+b22,注意平方和为定值,乘积有最大值,当且仅当a=b时取等号.若a、b∈R+,则有:(3)a+b≥2 ab%姨,乘积为定值,和有最小值,当且仅当a=b时取等号.(4)ab≤(a+b2)2,和为定值,乘积有最大值,当且仅当a=b 1. Knowledge has x2≥0 → (ab) 2≥0 → a2 + b2-2ab≥0, namely: (1) a2 + b2≥2ab, pay attention to the product as a fixed value, the sum of squares has a minimum value, if and only if (2) ab≤a2 + b22, note that the square sum is a fixed value, the product has the maximum value, if and only if a = b, take the equal sign.If a, b∈R +, then there is : (3) a + b≥2 ab% ai, the product is a fixed value, and there is a minimum, if and only if a = b take the equal sign. (4) ab≤ (a + b2) Value, the product has a maximum if and only if a = b