There are basic inequalities, absolute inequalities, Cauchy inequalities and quadrilateral inequalities in high school mathematics inequality formulas. Generally, pure greater than sign ">" and less than sign "are used.

1, the basic inequality: √(ab)≤(a+b)/2, can be transformed 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 | B |, ||| | A |-| B |≤| A |+| B |.

3. Cauchy inequality: if a 1, a2, …an, b 1, b2…bn are all real numbers, then (a1b1+a2b2+…+anbn) 2 ≤ (a1+anbn).

4. Quadrilateral inequality: For any a 1≤a2,

Principle:

1, the inequality f (x): F(x) is the same solution.

2. If it is inequality f (x)

3. If the inequality f (x): 0, then the inequality f (x)

4. Don't empty the equation F(x)G(x)>0 and inequality have the same solution; Inequality f (x) g (x)