A Novel Approach to Solving Irrational Equations via Symmetric Polynomials

In this article, we examine the use of symmetry groups for modeling applied problems through computer symbolic calculus. We consider the problem of solving radical equations symbolically using computer mathematical packages. We propose some methods to obtain a correct analytical solution for this class of equations by means of the Mathcad package. The application of symmetric polynomials is proposed to ensure a correct approach to the solution. Issues on the solvability based on the physical sense of a problem are discussed. Common errors in solving radical equations related to the specificity of the computer usage are analyzed. Provable electrical and geometrical problems are illustrated as example