a^2+b^2 ≥ 2ab .

√(ab)≤(a+b)/2 ≤(a^2+b^2)/2。

a^2+b^2+c^2≥(a+b+c)^2/3≥ab+bc+ac。

A+b+c≥3× cubic radical abc.

Mean inequality, also known as mean inequality and mean inequality, is an important formula in mathematics. The content of the formula is Hn≤Gn≤An≤Qn, that is, the harmonic average does not exceed the geometric average, the geometric average does not exceed the arithmetic average, and the arithmetic average does not exceed the square average.

Numbers in general inequalities are real numbers, and letters also represent real numbers. The general form of inequality is F(x, y, ..., z)≤G(x, y, ..., z? ) (in which inequality symbols can also be one of them), the common domain of analytical expressions on both sides is called inequality domain, which can represent both a proposition and a problem.

Generally, pure greater than sign ">" and less than sign "are used.

Among them, the common area of analytical expressions on both sides is called inequality area.

Algebraic expression inequality:

Both sides of the algebraic expression inequality are algebraic expressions (that is, the unknown is not on the denominator).

One-dimensional linear inequality: an unknown (that is, one dimension) and the degree of the unknown is 1 (that is, once). For example 3-x >0

Similarly, binary linear inequality: an inequality that contains two unknowns (namely binary) and the number of unknowns is 1 (namely once).