Rational and Radical Functions

Lesson 15

Math

Unit 4

11th Grade

Lesson 15 of 18

Objective


Solve radical equations and identify extraneous solutions.

Common Core Standards


Core Standards

  • A.REI.A.2 — Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Foundational Standards

  • A.REI.A.1

Criteria for Success


  1. Describe how a solution could be extraneous. 
  2. Explain how, when a radical equation has a variable outside of the radical, the result is a polynomial equation that must be solved. 
  3. Determine extraneous solutions from complex radical equations.
  4. Solve rational exponent equations either by converting to radical equations or by working with the rational exponents in their current form. 
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Anchor Problems

25-30 minutes


Problem 1

Solve the following equation: 
 

$${\sqrt{-3x-5}-2=x+1}$$

 

Guiding Questions

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Problem 2

Solve the following equation: 

 

$${(x-2)^{2\over3}=4}$$

 

Guiding Questions

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Target Task

5-10 minutes


Below are three answers to the problem $${{{{\sqrt{x-2}=2-x}}}}$$. Which answer is correct? Explain your reasoning. 

 

Answer #1 Answer #2 Answer #3

$${{{{\sqrt{x-2}=2-x}}}}$$

$${{x-2=4-4x+x^2}}$$

$${{0=6-5x+x^2}}$$

$${{x^2-5x+6=0}}$$

$${{(x-2)(x-3)=0}}$$

 

Solution: $${{x=2}}$$ and $${{x=3}}$$

$${{{{\sqrt{x-2}=2-x}}}}$$

$${x-2=4+x^2}$$

$${0=6-x+x^2}$$

$${x^2-x+6=0}$$

$${(x-3)(x+2)=0}$$

 

Solution: $${{x=3}}$$ and $${x=-2}$$

$${{{{\sqrt{x-2}=2-x}}}}$$

$${{x-2=4-4x+x^2}}$$

$${{0=6-5x+x^2}}$$

$${{x^2-5x+6=0}}$$

$${{(x-2)(x-3)=0}}$$

 

Solution: $${{x=2}}$$

 

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Solve rational equations.

Lesson 16
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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