Introduction to average inequality:
Also known as mean inequality and mean inequality, it 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.
Introduction to inequality:
The formula that uses the symbol ">" "< to represent the relationship between size is called inequality. An inequality represented by "≦" is also an inequality. Usually, the number in inequality is a real number, and letters also represent real numbers;
The general form of inequality is F(x, y, ..., z)≤G(x, y, ..., z) (in which the sign of inequality can also be one of them). The public domain of analytic expressions on both sides is called inequality domain, which can represent both a proposition and a problem.
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). Such as 3-x >0. Similarly, binary linear inequality: an inequality that contains two unknowns (namely binary) and the number of unknowns is 1 (namely once).
Basic nature:
If x>y, then y < x；; If y; y+z； (addition principle, or additivity of inequality in the same direction); If x>y, z>0, then xz & gtyz；; If x>y, z<0, and then xz.
If x>y, m>n, then X+M > y+n； (sufficient and unnecessary conditions); If x>y>0, m>n>0, then xm & gtyn；; If x>y>0, xn & gtYn(n is a positive number), xn