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Algebra 2

Course: Algebra 2 > Unit 10

Lesson 3: Extraneous solutions
Math
Algebra 2
Equations
Extraneous solutions
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Extraneous solutions of radical equations

Google Classroom
Practice some problems before going into the exercise.

Introduction

In this article we will practice some problems that involve thinking about the conditions for obtaining extraneous solutions while solving radical equations.

Practice question 1

Caleb is solving the following equation for x.
x, equals, square root of, x, plus, 2, end square root, plus, 7
His first few steps are given below.
x−7=x+2(x−7)2=(x+2)2x2−14x+49=x+2\begin{aligned}x-7&=\sqrt{x+2}\\ \\ (x-7)^2&=(\sqrt{x+2})^2\\ \\ x^2-14x+49&=x+2 \end{aligned}
Is it necessary for Caleb to check his answers for extraneous solutions?
Choose 1 answer:

Practice question 2

Elena is solving the following equation for x.
cube root of, 3, x, minus, 5, end cube root, plus, 2, equals, 7
Her first few steps are given below.
3x−53=5(3x−53)3=(5)33x−5=125\begin{aligned}\sqrt[3]{3x-5}&=5\\ \\ \left(\sqrt[3]{3x-5}\right)^3&=(5)^3\\ \\ 3x-5&=125 \end{aligned}
Is it necessary for Elena to check her answers for extraneous solutions?
Choose 1 answer:

Practice question 3

Addison solves the equation below by first squaring both sides of the equation.
2, x, minus, 1, equals, square root of, 8, minus, x, end square root
What extraneous solution does Addison obtain?
x, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Practice question 4

Which value for the constant d makes x, equals, minus, 1 an extraneous solution in the following equation?
square root of, 8, minus, x, end square root, equals, 2, x, plus, d
d, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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