Basic inequality is an inequality that is mainly used to find the maximum value of some functions and prove it. It means that the arithmetic mean of two positive real numbers is greater than or equal to their geometric mean.

Basic properties of common inequalities: a>b, b & gtc→a & gt；; c；

a & gtb→a+c & gt； b+ c；

a & gtb，c & gt0→AC & gt； BC;

a & gtb，cb & gt0，c & gtd & gt0→AC & gt； BD；

a & gtb，ab & gt0→ 1/ab & gt； 0→a^n>； b^n；

Basic inequality: √ (AB) ≤ (A+B)/2;

Then it can be changed to A 2-2 AB+B 2 ≥ 0;

a^2+b^2≥2ab。

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).