DOUBLE SUBSTITUTION FOR SOLVING EQUATIONS

Abstract

Double substitution is a method of solving equations, inequalities and problems with parameters containing equations and inequalities. This method is almost not presented in school textbooks of mathematics, problem books and reference books on elementary mathematics, but sometimes it turns out to be simpler than traditional methods for solving such problems commonly used in schools – exponentiation, factorization, and substitution. Here, double substitution will be applied to irrational equations. This method allows to do without raising the equation to a power, which in the case of even powers, is an inequitable transformation of the equation. An even more convenient technique is double substitution in inequalities and problems with parameters, examples of which we will give in the following papers.