√(ab)≤(a+b)/2

Then it can be changed to a 2-2ab+b 2 ≥ 0.

a^2+b^2 ≥ 2ab

Ab ≤ the square of the average of a and b

2. Absolute inequality formula:

| |a|-|b| |≤|a-b|≤|a|+|b|

| |a|-|b| |≤|a+b|≤|a|+|b|

3. Cauchy inequality:

Let a 1, a2, …an, b 1, b2…bn all be real numbers, then (a1b1+a2b2+…+anbn) 2 ≤ (a12+a22+).

4. Triangle inequality

Reinforcement inequality of any two vectors b

This inequality can also be called the triangle inequality of vectors.

5, quadrilateral inequality

If for any a 1 ≤ a2

There are m [a 1, b 1]+m [a2, B2] ≤ m [a 1, B2]+m [a2, b 1],

Then m[i, j] satisfies quadrilateral inequality.