Absolute Value Equations With The Unknown Under The Square Root

Abstract

Modular equations are one of the important and complex topics of algebra, which studies equations involving absolute value (modulus). The concept of modulus represents the distance of a number from zero, regardless of its sign. When solving modular equations, it is necessary to separate the expression into different cases based on the definition of modulus. This article discusses in detail the concept of modular equations, their types, main properties and solution methods. It also considers the issues of solving modular equations graphically and identifying typical errors. Studying the topic serves to develop students' logical analysis, conditional thinking and algebraic calculation skills, and serves as a solid theoretical basis for solving complex equations.