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Introduction.Improving the intellectual level, honing the ma-thematical preparation, the use of innovative approaches in solving a broad aspect of practical issues — this is the range of priority points in the study of mathematics. Practical solution of inequalities by non-traditional methods creates new opportunities for the formation of intuition, helps to increase the logic of thinking.
Materials and methods. Much of the college math program is devoted to the study of inequalities. The features of non-standard techniques in the study of irrational inequalities, based on the application of Cauchy and Bernoulli inequalities, are considered. Examples of solutions of irrational inequalities based on the use of the classical Cauchy and Bernoulli inequalities are given.
Results. The justified optimal choice of the method of solving inequalities in many ways helps the development of the student's thinking logic, contributes to the creative approach to finding a result.
Discussion. The use of non-standard ways to solve irrational equations and inequalities in the classroom contributes to an increase in the scale of academic performance, improves the level of mathematical logic. The use of classical Cauchy and Bernoulli inequalities in the study of irrational inequalities will give impetus to the research search of the questions posed to the student.
Conclusion. The use of classical Cauchy and Bernoulli inequalities in solving irrational inequalities and equations will increase the level of student knowledge. It will be easier for them to solve the tasks of increased difficulty, which will have an effect on the improvement of points on the Unified State Exam. The presented material will provide tangible methodological assistance to both teachers of mathematics with in-depth study of it, and students engaged in research activities.
mathematical education, mathematical competence, inequality, singularity, method, irrational inequality
Presents the main types of irrational inequalities;
The characteristic of the general methods of solving irrational inequalities is given;
Considered the features in solving irrational inequalities;
Cauchy and Bernoulli inequalities are presented;
Describes non-traditional application of Cauchy and Bernoulli inequalities to solving irrational inequalities;
The analogues of the inequalities included in the tasks of the Unified State Examination level are given.
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