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).