How to list equation problems, how to find formulas?

If you have time, you can send the questions you don't understand, and see how others do it, mainly to see how others list the equations, because each equation is an equal relationship, or a distance, or a time, or a quantity of engineering, etc., and you will learn it slowly by reading more and analyzing more. It should not be too difficult to look at each problem as a small story, understand the story, and then see how others analyze it.

If the two sides of the rectangle are x and y respectively, then x+y=18cm.

The side area of this cylinder is 2 xy, and 2 is a constant, which is actually the maximum value of x times y when x+y=18.

That is, x*y=x*(18-x)=-x 2+18x=-(x-9) 2+81 is the quadratic curve with the opening downward.

This shows that when x=9, the equation has a maximum value of 81. and y=18-x=9.

Finally, when the length and width of the rectangle are 9 (cm), the maximum area of the cylindrical side is 162 (cm 2).

Column equation solution application steps:

1. Practical problems (review the problem, clarify all known and last known conditions and quantitative relationships).

2. Let the last known number (generally set directly, sometimes indirectly), and use the algebraic formula of the last known number to represent all the last known quantities.

3. Find the equation of the equivalence off.

4. Solve the equation and find other final conditions.

5. Test (test whether it is the solution of the original equation and whether it conforms to the practical significance).

6. Answer. Focus: Examination of questions. The key: use the algebraic formula of the last known number to represent all the last known quantities, and find the equivalent relation.

The column equation method is as follows:

2: Find out the relationship between the various quantities given in the question;

3: Set unknowns; It doesn't have to be a straightforward unknown

4: According to the sum or difference or multiple relationship provided in the problem, list the corresponding equations, that is, equations;

5: Solve the equation and check the sum operation.

2: Find out the relationship between the various quantities given in the question;

3: Set unknowns; It doesn't have to be a straightforward unknown

4: According to the sum or difference or multiple relationship provided in the question, list the corresponding equations, i.e., equations;

5: Solve the equation and check it.

Generally, what is sought is set as x, and then according to the known conditions, the equivalence relationship is found and the equation is listed.

The most important point of the column equation is to find the equivalence relationship, read the question carefully, and find the keywords, for example: the first class is more than the second class 1 3, then the second class x is set, then the first class is (1+1 3)x, both of which are equal to known conditions, and the column equation is simple.

Set up the unknowns, and then use the known conditions to list the equations, the key is to find the equation relationship in the problem.

List the known quantities, and then list the equations according to the requirements of the question.

Understand the topic. Read the question carefully, understand the meaning of the question, and understand the known conditions and the questions you are asking for.

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Analyze the problem. If it is a fraction problem, you can draw a line diagram to help you understand.

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Find equiquantitative relationships. This is the key step in solving this kind of problem, and finding the equivalence relationship in the problem is the most important step. It is also a difficult point for this kind of problem.

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Column equations, solving equations. Set the unknown to a letter, usually x, according to the equation of the equivalence off series, and solve the equation.

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Inspection. The process of testing is something that students tend to overlook, but it is an important step that can only be done after testing to determine whether the answer is correct or not. Generally, the answer is regarded as the original meaning of the person with the known conditions, and the calculated result is correct if it is consistent with the original condition, otherwise it is wrong.

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Write out the answer. This is the last and indispensable step in solving the problem of column equations.

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Step 1. Column equivalence relation. This must be listed, if not, the simple questions may be done, but the difficult questions may not be done.

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Step 2. Analysis, the general problem will have more than two equal relations, generally with the simple solution and the complex column equation.

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Step 3. Unraveling, for example, is to set what is x, then what is y step 4. Equations are listed according to the equiquantitative relation.

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Step 5. Solve equations.

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Step 6. Check, this step must be written to verify that you are doing it correctly. The general approach is to evaluate by substitution.

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Step 7. Answer.