New Approach to Solving Irrational Equations and Inequalities

The article examines the current state of mathematics development, its impact on the competence and level of knowledge of modern schoolchildren, reveals the importance of logical rigor for mastering mathematical skills and the ability to think creatively. The emphasis is on the need to apply mathematical knowledge in solving non-standard problems, as well as on the development of an analytical mindset. The influence of mathematical Olympiads and nationwide testing on the formation of students' deep mathematical skills and logical thinking is investigated. The main role in the research is given to a new approach to solving irrational equations and inequalities, the application of which leads to the development of logic, intuition, creative thinking, and also allows you to answer questions not only from various branches of mathematics, but also in physics and chemistry. The main stages of a new approach to solving irrational equations and inequalities are determined, and the effectiveness of using some types of irrational equations and inequalities in solving is noted.