Using restrictions to accept or reject solutions of radical equations

Authors

Eleftherios Gkioulekas, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

4-16-2018

Abstract

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation. In this article, we review previous literature, establish and illustrate rigorous solution procedures for radical equations of depth 1 (i.e. equations where all radicals can be eliminated in one step), and deal with an ambiguity concerning the definition of real-valued solutions to radical equations. An application to defining the inverse function, resulting in a parametric radical equation, is also explained.

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology on 2018 available online: http://www.tandfonline.com/10.1080/0020739X.2018.1458341

Recommended Citation

Eleftherios Gkioulekas (2018) Using restrictions to accept or reject solutions of radical equations, International Journal of Mathematical Education in Science and Technology, 49:8, 1278-1292, DOI: 10.1080/0020739X.2018.1458341

Publication Title

International Journal of Mathematical Education in Science and Technology

DOI

10.1080/0020739X.2018.1458341