In high school inequality, there is a common inequality ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2 There is a common inequality in senior high school, which is ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2. Is there any difference between [(a + b) / 2] &# 178; and (a & # 178; + B & # 178;) / 2, or is it equal?

In high school inequality, there is a common inequality ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2 There is a common inequality in senior high school, which is ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2. Is there any difference between [(a + b) / 2] &# 178; and (a & # 178; + B & # 178;) / 2, or is it equal?

The two inequalities are correct. They are used in different cases, but the scope of AB is different. For example, ab = 3, the value of [(a + b) / 2] &# 178; is 4, and the value of [(A & # 178; + B & # 178;) / 2 is 5. Both of them are true
PS: ab ≤ [(a + b) / 2] &# 178; and ab ≤ (A & # 178; + B & # 178;) / 2 are derived from (a-b) &# 178; ≥ 0, but [(a + b) / 2] &# 178; ≤ (A & # 178; + B & # 178;) / 2