Why are equations so difficult, and are they so difficult to solve? Why am I so confused?

If you're solving equations, just figure out the key to each step. If it is a column equation solving problem, you just need to grasp the equivalence relationship of each type of problem. As long as you put a lot of effort into it, I believe you will definitely learn well. Come on.

Solution: Equations are not difficult at all, and the equations in our textbooks have systematic solutions and root formulas. In practical problems, it is easy to establish equations as long as you find an equiquantity relation.

Please refer to it. Equations containing unknown quantities are equations, mathematics was first developed in counting, and about numbers and unknowns are combined by addition, subtraction, multiplication, division, and idempotency to form algebraic equations: unary equations.

Unary quadratic equations, binary quadratic equations.

Wait a minute. However, with the emergence of the concept of functions and the introduction of function-based differentiation and integration operations, the scope of equations has become more extensive, and unknown quantities can be mathematical objects such as functions and vectors, and operations are no longer limited to addition, subtraction, multiplication and division.

Equations occupy an important place in mathematics and seem to be an eternal topic in mathematics. The emergence of equations not only greatly expanded the scope of mathematical applications, enabling many problems that could not be solved by arithmetic problem solving, but also had a great impact on the progress of mathematics in the future. In particular, many major discoveries in mathematics are closely related to it.

In middle school, the equations that I came into contact with were basically in this category, and the unknowns in the equation could appear in the fractions and integers in the equation.

Radicals and trigonometric functions.

in the independent variables of elementary functions such as exponential functions.

The formula for finding the root of a quadratic equation.

In secondary school, when you encounter the problem of solving equations, in general, you can convert the equation into a whole Limin equation; Generally, it is converted into a one-dimensional quadratic equation, or a system of multivariate one-dimensional equations.

Ordinary differential equation.

Solve the functional and find the fastest curve.

Issue. Since mathematics from constants.

Mathematics is transformed into variable mathematics, and the content of equations is also enriched, because mathematics introduces more concepts, more operations, and thus more equations. The development of other natural sciences, especially physics, has also directly put forward the need for equation solving, providing a large number of research topics.

First of all, we need to know that the meaning of equations is that the equations that express equality relations are called equations, and equations that contain unknowns are called equations. It can be seen that the equation must meet two conditions: first, the equation; The second is that there must be unknowns in the equation.

1. Use the properties of equations to solve equations.

Because the equation is an equation, the equation has the properties that the equation has.

1. Add or subtract the same number from the left and right sides of the equation at the same time, and the solution of the equation remains unchanged.

2. The left and right sides of the equation are multiplied by the same non-0 number at the same time, and the solution of the equation remains unchanged.

3. The left and right sides of the equation are divided by the same non-0 number at the same time, and the solution of the equation remains unchanged.

2. The solution of the equation for two-step and three-step operations.

The two-step and three-step equations can be calculated according to the properties of the equation, and the original guess remainder equation is first converted into a one-step solution equation, and the solution of the equation is solved.

3. Solve the equation according to the relationship between the parts of addition, subtraction, multiplication, and division.

1. Solve the equation according to the relationship between the parts in the addition.

2. Solve the equation according to the relationship between the parts in subtraction.

In subtraction, being decelerated = difference + subtraction.

3. Solve the equation according to the relationship between the parts in multiplication.

In multiplication, one factor = product of another.

4. Solve the equation according to the relationship between the parts in the division.

After solving the equation, it is necessary to verify that the solution is true through a test. To see if the number on the left side of the equation is equal to the number on the right side of the equation, the value of the unknown number is substituted into the original equation. If the numbers are equal, the value is the solution of the original equation, and if the numbers are not equal, it is not the solution of the original equation.

The above methods are commonly used methods and techniques in primary school mathematics, and I hope that students will practice more and master them proficiently.

When solving equations, such a problem is actually relatively simple and simple, and we have some thinking formulas, but relatively speaking, it is not difficult to master its operation method.

It's not hard to pay attention to the process at all.

The most difficult equations include the famous Fermat's theorem, Fermat's implicit conjecture, and a three-circle problem that has puzzled scholars.

1. The famous Fermat's theorem.

x n + y n = z n, where x, y, z, n are positive integers, and n>2. This equation is considered the "holy grail" in the field of number theory, and Andrew Wiles, who solved the problem of Fermat's theorem, also won the Fields Prize.

2. Fermat Qingsen Ger's implicit conjecture.

This is a mathematical conjecture that attempts to prove a special case of Fermat's theorem. The Beckermann conjecture and the Donaldson Wolfram conjecture are considered to be two variants of Fermatger's implicit conjecture.

3. A three-circle problem that bothers scholars.

Three circles on a plane, perpendicular to each other, and with unequal radii, whether there are half-lines that can cut the three circles separately. This issue has not been resolved to this day.

It should be noted that the above equations do not represent the most difficult equations in all mathematics, because the field of mathematical knowledge is too broad, and if you look at other fields**, there may be other more complex equations.

Introduction to Fermat's Great Theorem:

Fermat's Great Theorem, also known as Fermat's Last Theorem, states that for any integer n greater than 2, there are no integers a, b, and c that make a n + b n = c n true.

Fermat's theorem is a well-known problem in mathematics, which was proposed by the French mathematician Fermat in the 17th century, but has never been proven. Fermat himself stated in his manuscript that he had a method of proof, but this method was never made public. After centuries of hard work and exploration, it was not until 1994 that the British mathematician Andrew Wiles gave the proof of this book hole problem.

Wiles' proofs are incredibly complex and involve a wide range of disciplines, including algebraic geometry, harmonic analysis, differential geometry, number theory, and many other fields.

The proof of Fermat's theorem caused a huge sensation, and Wildazimus was awarded the Fields Medal, one of the highest awards in mathematics. The proof of Fermat's theorem is of great significance to the development of the field of mathematics, which not only proves the correctness of a mathematical problem, but also promotes the in-depth study of mathematics and opens up a new direction for mathematical research.

The equations that are particularly difficult to solve are as follows:

1. Equations of the higher order difference series:

Such equations often require the use of advanced mathematical techniques and methods to solve, such as summation formulas and general term formulas.

2. Higher-order proportional equations:

Such equations often require the use of advanced mathematical techniques and methods to solve, such as summation formulas and general term formulas.

3. Complex one-dimensional quadratic equations

Such equations usually require knowledge of the discriminant formula of the root and the relationship between the root and the coefficients.

4. Multivariate quadratic equations:

Such systems of equations usually need to be solved using methods such as substitution or addition and subtraction.

5. Solving equations:

Solving an equation is the process of solving an equation for one or more unknowns. An equation is an equation between one or more unknowns and constants, and the purpose of solving an equation is to find the value of the unknown and make the equation true.

Solving equations usually requires the use of mathematical methods and techniques, such as algebra, equations, equal difference series, proportional series, etc., to solve the equation.

How to learn math well:

A high forest car, establish a good foundation:

The first step in learning math well is to build a good foundation. Before learning new math concepts, you need to make sure that you have mastered the fundamentals and skills. Make sure you have a clear understanding of the foundational concepts and skills.

If there are any weak points in the basics, they should be supplemented and consolidated in a timely manner.

3. Qi Xi asks for help:

If you get stuck, you can seek help from your teacher or classmates. They can provide guidance and advice to help you better understand math concepts and methods. Think more, learning math requires a lot of thinking. You can try different ways of thinking about the problem and try to solve the problem on your own.

Plan well: Learning math requires a good plan. You can make a study plan and schedule your time and energy to study math according to the plan.

Conduct regular self-assessments to see where you've made progress and what needs to be strengthened. Adjust your study plan in a targeted manner.

I've written too much about the steps of solving the equation.

You can simplify the steps.

What is the use of solving equations?

It is recommended to find some difficult questions to do.

Ordinary differential equations: y'+ 4y+ 4=0, if you can write, you will have a second ......

Solution: (3x-7) 5=16

3x-7=16×5

3x-7=80

3x=87x=29

Test: Left = (3 29-7) 5 = (87-7) 5 = 80 5 = 16 Right = 16 Left Regret Front=Right.

So x=29 is the solution of the original equation.

Solution Analysis: A general method for solving the unary one-dimensional Biqing equation:

1. Remove the denominator from the slippery potato.

2. Remove parentheses.

3. Move items, 4. Merge similar items.

5. The coefficient is 1

6. Inspection.