Question

When is it necessary to check for extraneous solutions?

   When is it necessary to check for extraneous solutions?

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 2

Instant Answer

Solved by Expert Brandon Cleary

07/16/2021

Step 1

Extraneous solutions are solutions that are derived from the process of solving the equation but are not valid solutions to the original equation. They often arise when we square both sides of an equation or when we solve rational equations. Show more…

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When is it necessary to check for extraneous solutions?

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Key Concepts

Extraneous Solutions

Extraneous solutions are those that arise from the process of solving an equation but do not satisfy the original equation. They often occur as a result of algebraic manipulations and must be checked to ensure they are valid within the original constraints of the problem.

Domain Restrictions

Domain restrictions refer to the limitations placed on the variable values by the original equation, such as restrictions imposed by even roots, logarithms, or denominators in rational expressions. Solutions that fall outside these restrictions are considered extraneous.

Algebraic Manipulations That Introduce Extraneous Solutions

Certain algebraic operations, such as squaring both sides of an equation or multiplying by expressions that could be zero, can introduce extraneous solutions. These steps should be followed by verifying each obtained solution against the original equation to ensure that no invalid solutions are accepted.

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