(1) Classification discussion method: according to the positive, zero and negative scores of numbers or formulas in absolute value symbols, the absolute value is removed.
(2) Zero-paragraph discussion method: it is suitable for the case that multiple absolute values contain one letter.
(3) Bilateral flattening method: it is suitable for equations or inequalities with non-negative edges.
(4) Geometric meaning method: it is suitable for the situation with obvious geometric meaning.
2. It is an important skill to choose the method according to the number of terms and follow the general steps.
3. Using the complete square formula to change a formula or part into a complete square is the matching method, which is an important method and skill in mathematics. The main basis of the matching method is:
4. method of substitution is used to solve some complicated special equations. The general steps of solving equations by substitution method are:
5. The undetermined coefficient method is a method to find the object under the condition that the shape of the object is known. It is suitable for solving some important problems, such as coordinates, resolution function and curve equation.
Basic properties of inequality:
The basic properties of inequality are symmetry, transitivity and additive monotonicity, that is, the additivity of inequality in the same direction; Multiplicative monotonicity; Multiplicity of positive inequality in the same direction; Multiplier of positive inequality; Positive inequalities can be solved; The law of reciprocity.
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 the inequality symbol can also be one of them).
The common domain of analytic expressions on both sides is called inequality domain, which can represent both a proposition and a problem.