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Solving Radical and Higher-Degree Equations: Methods and Techniques

This lesson focuses on solving equations that involve radicals and higher-degree variables. It outlines how to transform radical equations into quadratic forms and emphasizes the importance of isolating radicals before squaring both sides. The content discusses the potential for extraneous solutions and highlights the use of graphing calculators to find intersections and verify solutions. Additionally, techniques for rewriting higher-degree equations in terms of second-degree variables are presented, providing learners with effective methods for solving diverse equation types.

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Solving Radical and Higher-Degree Equations: Methods and Techniques

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  1. Lesson 2-3 cont’d Radical Equations and Higher Degree Equations Click here to add text Click here to add text. Click here to add text. Click here to add text. Click here to add text. Click here to add text. Click here to add text. Objective: To solve equations involving radicals and higher degree variables.

  2. Radical Equations Radical equations can be transformed into quadratics to solve.

  3. Solve Isolate one of the radicals before squaring both sides

  4. Solve:

  5. EXAMPLE 2 2 ( ) NO SOLUTION Since 16 doesn’t plug in as a solution. Note: You will get Extraneous Solutions from time to time – always do a quick check Let’s Double Check that this works

  6. Can graphing calculators help? SURE! • Input for Y1 • Input x-2 for Y2 • Graph • Find the points of intersection One Solution at (4, 2) To see if this is extraneous or not, plug the x value back into the equation. Does it work?

  7. Higher Degree Equations Higher degree equations can be solved using quadratic methods Rewrite the equation in terms of a second degree variable

  8. Solve the following equation: We can rewrite the equation in terms of x2. Substitute u to represent x2. Solve using a quadratic method. Put the x2 back in for u.

  9. Solve

  10. Sources • www.pleasanton.k12.ca.us • www.dgelman.com/powerpoints • http://www.mrperezonlinemathtutor.com/private2/ALG_PDF_FILES/7_3_Quadratic_Techniques_Solving_Polynomial_Eq.pdf

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