I. Definition of Equation
An equation with unknowns. It is an equation that represents the equal relationship between two mathematical expressions (such as two numbers, functions, quantities and operations), and the value of the unknown quantity that makes the equation hold is called "solution" or "root".
Equation usually consists of unknown quantity, known quantity, operator and equal sign. Unknown quantity refers to the quantity we want to solve, usually expressed in letters, such as x, y, z, etc.
A known quantity is a known quantity, which can be a number, a constant or other variables. Operators include addition, subtraction, multiplication and division. They are used to calculate the relationship between unknown quantities and known quantities. The equal sign is used to make the expressions on the left and right sides equal.
Second, the type of equation.
Equations can be divided into univariate equations and multivariate equations. The unary equation has only one unknown number, such as x+3 = 5. A multivariate equation has two or more unknowns, such as x+y = 5.
Equations can also be divided into linear equations and nonlinear equations. A linear equation means that the degree of the unknown quantity is 1, for example 2x+3 = 7. A nonlinear equation refers to an unknown quantity with a degree greater than 1, such as x 2+2x+1= 0.
Third, the application of the equation
Equations are widely used in mathematics, including algebra, geometry, physics, engineering and other fields.
The solution of the equation can help us solve various problems, such as calculating the area of the house, calculating the speed and acceleration of the object, and calculating the mass of the object in the chemical reaction. In practical application, we usually use computer software and algorithms to solve equations, such as MATLAB, Mathematica and Python.
General method of solving equations
1, estimation method
An introductory method when you are just learning to solve equations. Estimate the solution of the equation directly, and then substitute it into the original equation for verification.
2. Apply the properties of the equation to solve the equation.
3. Merge similar projects
Turn an equation into a monomial.
Step 4 move the project
Move the unknown term to the left and the constant term to the right.
5. Remove the bracket
Use the rule of removing parentheses to remove parentheses from the equation.
6. denominator
Multiply both sides of the equation by the least common multiple of all denominators at the same time.
7. Formula method
For some equations, the general form of the solution has been studied and become a fixed formula, which can be used directly.