# Methods of solving equations and equations

## Introduction

"Methods for Solving Equations and Equations" is published by Anhui Normal University Press.

## Book catalog

Foreword

General introduction

1 factorial method

2 substitution method

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1. Single-type conversion method

2. Difference and constant conversion method

3. Mean value conversion method

Four. Cycle conversion Element Method

3 Proportional Nature Method

4 Non-negativity Method

1. Apply the non-negativity of even-order arithmetic roots

2. Use the nonnegativity of absolute value

3. Use the nonnegativity of even power or even root of real numbers

5 inequality method

1. Using mean inequalities

2. Using inequalities to determine or define the roots of equations (groups)

6 Basic solutions for elementary transcendental equations

1. Exponential equation

2. Logarithmic equation

3. Power function equation of irrational exponent

4. The simplest triangle equation

5. The simplest equation of inverse trigonometric function

7Using the root and coefficient relationship method

8 matching method

9Constructing auxiliary formula or auxiliary equation (group) method

1. Conjugate factor method

2. Apply the same solution theorem to construct auxiliary equations

3. Use square method to construct auxiliary equations

Four. Construct the auxiliary equation from the consistency of the equation structure

Five. Construct the auxiliary equation from the symmetry of the equation (set)

VI. Construct the auxiliary equation from the given conditions and functions The nature of the construction of auxiliary equations

Seven, the use of triangular duality to construct auxiliary equations (sets)

10 discriminant method

11 formula method

< p>1. Formula method for root extraction

2. Formula method for root finding

3. Inverse usage of formula for root finding

Four. Formula method for multiplication

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5. Cramer formula method

12 multiplication method

13 uniqueness method

1. Using irrational number expression form Uniqueness

2. When using complex numbers to be equal, the uniqueness of the corresponding equal parts of the real and imaginary parts

3. The uniqueness of using fractions to transform into continued fractions

< p>Four. Use the same number of powers to equal the sum of isomorphic terms, and the uniqueness of the corresponding exponents

Five. Use the same number of fractional isomorphic terms to equal the sum, the numerators correspond to the same, and the uniqueness of the denominator The rational root method of 14 rational coefficient equations

15 triangle substitution method

16 fraction equation deformation method

1. True Fraction method

Two. Multiplying common denominator and rounding method

Three. Reduction method

Four. Substitution method

Five , Proportion Method

Six. Discussion Method

Seven. Partial Fraction Method

8. Subsection Method Method of division

Nine. Determinant method

17 Zero point subsection method

18 Constant and variable interchange method

19 Equation group Elimination method

1. Substitution elimination method

2. Comparative elimination method

3. Addition and subtraction elimination method

4. Gaussian Elimination Method

Auxiliary Angle Method of 20 Triangular Equations

21 Accumulation and Multiplication

22 Resultant Method

23 Solving method of symmetric equation system

1. Solving method of first kind of symmetric equation system

2. Solving method of second kind of symmetric equation system

24 division method< /p>

25 reciprocal equation solutions

1. Types and properties of reciprocal equations

2. Reciprocal equation solutions

26 open methods< /p>

27 definition domain and value range discussion method

28 function monotonicity method

29 geometry method

30 indefinite equation solution

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One, two-variable first-degree indeterminate equations

Second, multiple-variable first-degree indefinite equations and equations

Three. Pell equation solution

Four. The solution of the Pythagorean equation

Five. The rational ratio method for solving the indefinite equation xy =22

VI. The solution form is ay2 = x(x+1) quadratic indefinite The recursive method of the equation

Seven. The parity analysis method for solving the multivariate high-order indeterminate equation

31 The method of solving linear congruence equations

1. Congruence The concept and properties of the formula

2. Residual class and complete residual system

3. Simplified residual system

4. Euler theorem, Fermat theorem, Wilson theorem< /p>

Five. The solution of linear congruence equations

VI. The solution of first-order congruence equations

Conclusion

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