Using the parameter method while solving some types of non-standard equations

Abstract

The parameter method for solving non-standard tasks is discussed. Using this method simplifies solving some types of non-standard equations. The essence of the method is follow: to solve the equation, we use a parameter and see an equation containing a much more general type of parameter than the solvable equation, from which the solvable equation is received for the specific value of the parameter. We solve the equation containing the parameter and then return to solve the given equation for the specific value of the parameter on which the parametric equation matches the solvable equation. By using such an approach, it becomes necessary to determine the set of allowable values of the equation, because the transition from the solvable equation to the equation containing the parameter sometimes expands the set of allowable values of the variable, and it is possible to have an extraneous root. The solution of different types of non-standard equations using the parametric method is discussed and the advantages of its use over other methods of solving non-standard problems are substantiated.