IRRATIONAL EQUATIONS AND METHODS FOR SOLVING SYSTEMS OF EQUATIONS

This article examines the problem of solving irrational equations and systems of equations. The paper first analyzes the essence of the concepts of irrational numbers and irrational equations, highlighting the methodological aspects that should be considered when teaching these topics in the school algebra course. It provides a detailed explanation of the methods for determining the domain of definition, rationalization, raising both sides of an equation to the same power, and introducing new variables. In addition, using examples of equations containing square root expressions, the causes of extraneous roots are analyzed. The article presents step-by-step procedures for solving irrational equations and systems of equations, including defining the domain, substituting variables, raising to powers, and verifying solutions. As a result, the study contributes to improving the methodology of teaching irrational equations in school algebra, developing students’ logical thinking, and deepening their mathematical reasoning.