How to choose the appropriate solution to solve quadratic equations is a difficulty encountered by many students. In fact, as long as we can consolidate and master the four solutions to quadratic equations and gradually increase the difficulty of the questions, Develop your numeracy and calculation skills, and quadratic equation problems will be easy to solve. The following is a selection of 20 typical example questions, with detailed problem-solving procedures. Through training, the method of substitution can be used flexibly to embody the mathematical idea of turning the unknown into the known.
Question 1: Solve the equation: 4(x-1)2 =25. This problem can be solved using the direct square root method. The problem-solving process is shown in the figure below:
Question 2. Solve the equation:
Question 3: Solving Equations
Question 4: Solving Equations
Questions 5-6: Solving Equations< /strong>
Questions 7-8: Solving Equations< /strong>
Question 9: Solving Equations
Question 10: Solve the equation (x-5) (3x- 2)=10
Question 11: Solving Equations
Question 12: Solving Equations
Question 13: Solve the equation: (x+2)(x +3)(x-4)(x-5)-44=0
One of the basic ideas in solving equations is to "reduce the degree", for example, convert one variable into two The linear equation is reduced in degree and converted into two linear equations of one variable. This problem turns out to be a fourth degree equation of one variable. Let's try to see if we can use the factorization method.
Question 14: Solve the equation: (3x+2)2- 8(3x+2)+15=0
When solving this problem, it is not appropriate to combine (3x+2)2 and 8(3x +2) Expand and organize it into the general form of a quadratic equation.
Careful observation of the structure of the question shows that if 3x+2 is replaced by t, then The original equation is the quadratic equation of t t2-8t+15=0.
Question 15: Use the matching method to solve the following equations
Question 16: Use formulas to solve equations
Question 17: Solving Equations
Question 18: Solving Equations
Question 19: Use formulas to solve equations
Question 20: Use formulas to solve equations
There are four methods for quadratic equations of one variable, namely direct square root method, factor Decomposition method, combination method, root formula method. (ax2+bx+c=0; ax2+bx=0, ax2+c=0, ax2=0) By changing elements and reducing order, turning the unknown into the known is an important idea for solving equations.
There may be multiple solutions to the same question, and we should choose one based on the structure of the question Appropriate solution. During the problem-solving process, calculation skills should be used based on calculation. The calculation process should be as simple and reasonable as possible. You should have the perseverance to calculate to the end, and check for possible errors at any time during the problem-solving process.
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