Matching method
Is to collect numbers.
Alternative method
When solving mathematical problems, a formula is regarded as a whole and replaced by a variable, thus simplifying the problem. This is called substitution. Methods include: local replacement, triangle replacement, mean replacement, etc. Local substitution, also known as global substitution, means that an algebraic expression appears many times in the known or unknown, and it is replaced by a letter to simplify the problem. Of course, sometimes it is discovered through deformation. For example, to solve the inequality: 4+2-2 ≥ 0, first transform it into 2 = t(t >；; 0), and familiar with solving quadratic inequalities and exponential equations.
Triangular substitution is used to remove the root sign, or when it is easy to find the triangular form, it is mainly to use a certain point in the known algebra for substitution. If the range of function y =+ is found, it is easy to find x∈[0, 1]. Let x = sin α, α ∈ [0,0], and the problem becomes the range of trigonometric functions that everyone is familiar with. Why did you think of this setting? Mainly to find the relationship between the range of values and the need to remove the root sign. For example, the variables x and y apply to the condition x+y = r (r >; 0), x = rcos θ and y = rsin θ can be transformed into trigonometric problems by trigonometric substitution.
method of undetermined coefficients
A way to discover the unknown. The general usage is that all or part of the coefficients of a polynomial are unknown, and these coefficients are determined by using the principle that the coefficients of two polynomials are equal in the same category or other known conditions, so as to get the value to be found. For example, if a known polynomial is decomposed into factors, the coefficients of some factors can be set as unknowns, and these unknowns can be obtained by using the conditions of identities. The undetermined coefficient method can also be used to solve the conic equation that has passed some points. In a broader sense, the undetermined coefficient method is a method to solve the problem by taking some constants of an analytical formula as unknowns and using known conditions to determine these unknowns. This method can be used to find the expression of function, decompose a rational fraction into the sum of several simple fractions, and find the solution of differential equation in series form.
An equation composed of three different letters usually has three ternary linear equations to solve the unknown solution.
Their main features are addition, subtraction and substitution elimination. Generally, addition and subtraction are used to eliminate elements, and substitution is used to eliminate elements if the equation is difficult to solve, which varies from topic to topic.
There are three unknowns, the degree of the term containing the unknowns in each equation is 1, and a * * * has three equations, which is called a ternary linear equation.
Trivariate linear equations are generally studied in the function of third-grade mathematics.
Assignment method is to assign certain special values to some letters in algebraic expressions (or equations or function expressions), so as to achieve the purpose of solving problems easily. Assignment method actually embodies the idea of transforming from general to special, which is very common in college entrance examination questions, especially in binomial theorem. Now give an example.
Example1if (1-3x) 9 = a0+a1x+a2x2+…+a9x9, then | a0 |+| a1| | a2 |+…| a9 | = _ _
The solution shows that a0, a2, …, a8 are positive, and a 1, a3, …, a9 are negative, so | A0 | +| A1|| A2 |+…+| A9 | = A0-a1+A2-A3.
In the given expansion, let x =- 1
| A0 |+| a 1 |+| a2 |+…+| a9 | = A0-a 1+a2-a3+…+A8-a9 =[ 1-3(- 1)]9 = 49