1, basic inequality:

√(ab)≤(a+b)/2, then it can be changed into the square of the average value of a 2-2ab+b 2 ≥ 0, a 2+b 2 ≥ 2ab, AB≤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

For the reinforced inequality of any two vectors b, this inequality can also be called the triangular inequality of vectors.

5, quadrilateral inequality

If for any a 1 ≤ a2

Basic attribute

(1) if x>y, then y < x；; If y

2 If x>y, y & gtz；; So x>z (transitivity).

③ if x>y and z is any real number or algebraic expression, then x+z >; Y+z (addition principle, or additivity of the same inequality).

4 If x>y, z>0, then xz & gtyz；; If x>y, z<0, and then xz.

⑤ If x>y, m>n, then X+M > Y+n (necessary and sufficient conditions and unnecessary conditions).