**M.M. Isakova**ORCID

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**R.G. Tlupova**ORCID

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**F.A. Erzhibova**ORCID

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**A.S. Ibragim**ORCID

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**Non — traditional methods of irrational equations decisions**

**Abstracts**

*Introduction.* Mathematics, like other subjects of the general education profile, aims at raising the general intellectual level, special mathematical training, developing a creative approach to solving the questions posed. During the study and practical solution of the equations, there are ample opportunities to form intuition, increase the logic of thinking.

*Materials and methods. *An extensive part of the mathematics program at the college is devoted to the study of equations. A particular case of algebraic equations is irrational equations. Described unconventional methods for solving irrational equations are based on the application of the Cauchy and Bernoulli inequalities. Equations with complete solutions based on the use of the indicated inequalities are presented.

*Results. *The solutions of irrational equations are the most difficult for students, not only in logic, but also in engineering. Their undisputed solution largely predetermines the successful result of the profile level of the USE. The psychological and pedagogical conditions for mastering non-traditional ways of solving irrational equations are considered.

*Discussion.* The use of non-standard ways of solving irrational equations in the classroom helps to increase the scales of achievement, improve the level of mathematical logic.

*Conclusion. *Students who have mastered non-traditional ways of solving irrational equations will successfully cope with tasks of increased complexity. The presented material can be a help in the work of teachers of specialized mathematical classes and provide significant assistance to the students.

**Keywords**

equation, inequality, method, irrational equation, logic

**Highlights**

- The main types of irrational equations are considered;
- Characteristics of general methods for solving irrational equations are given;
- Inequalities of Cauchy and Bernoulli are presented;
- The non-traditional application of the Cauchy and Bernoulli inequalities to the solution of irrational equations is shown;
- Analogues of equations with solutions included in the profile level of the USE are presented.

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