"End-of-Chapter Review Improvement Course" Quadratic Functions, Equations and Inequalities of One Variable PPT

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"End-of-Chapter Review Improvement Course" Quadratic Functions, Equations and Inequalities of One Variable PPT

Comprehensive improvement

Application of Inequality Properties

(1) Which of the following propositions is correct ()

①If a>1, then 1a<1; ②If a+c>b, then 1a<1b; ③For any real number a, a2≥a; ④If ac2>bc2, then a>b.

A． 1 B. 2

C. 3 D. 4

(2) Given that 2

regular method

When judging the true or false of a proposition about an inequality, first connect the proposition to be judged with the properties of the inequality, find properties similar to the proposition, and use the properties to determine the true or false of the proposition. Pay attention to the application of the special value method in solving objective problems related to inequalities.

It is known that a, b, c∈R, then the correct one of the following propositions is ()

A． If a>b, then ac2>bc2

B． If ac>bc, then a>b

C. If a3>b3 and ab<0, then 1a>1b

D. If a2>b2 and ab>0, then 1a<1b

Analysis: Choose C. When c=0, we know that A is incorrect; when c<0, we know that B is incorrect; from a3>b3 and ab<0, we know that a>0 and b<0, so 1a>1b is true, C is correct; when a<0 and b<0, it can be seen that D is incorrect.

basic inequalities

If x>0, y>0, and x+2y=5, find the minimum value of 9x+2y, and find the values ​​of x and y when the minimum value is obtained.

[Analysis] Because x>0, y>0, and x+2y=5,

So 9x+2y=15(x+2y)9x+2y

=1513+18yx+2xy

Solving strategy

Problem-solving strategies for optimal value problems of conditional inequalities

(1) The use of conditions is the key to solving such problems. Commonly used methods include substitution, substitution of "1", etc. When solving problems, you must also pay attention to the restrictions on letter values ​​during the deformation process, otherwise it may affect the results. The value of the letter when equal sign.

(2) It is also crucial to deform the equation that requires the optimal value. Commonly used methods include matching method, element substitution method, etc. The principle is to construct a fixed value. During the problem-solving process, you should also pay attention to the fact that the equal sign must be obtained. Otherwise this deformation is wrong.

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Update Time: 2024-09-27

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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