Question

Explain what an extraneous solution is.

   Explain what an extraneous solution is.

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 12, Problem 2

Instant Answer

Solved by Expert Charles Carter

04/21/2020

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Step 1: First, we start with the original equation, which is $\sqrt{x} = -2$. Show more…

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Explain what an extraneous solution is.

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Key Concepts

Extraneous Solution

An extraneous solution is a value that emerges from the process of solving an equation but does not satisfy the original equation when substituted back in. This occurs because certain algebraic manipulations, such as squaring both sides or multiplying by expressions that may be zero, can introduce solutions that seem valid in the transformed equation but are not valid in the context of the original problem.

Solution Verification

Verification of solutions is an essential step in solving equations, especially when manipulations can introduce extraneous solutions. By checking each potential solution in the original equation, one can determine whether it truly satisfies the equation or if it is an artifact of the algebraic process.

Domain Constraints

Domain constraints play a crucial role in determining the validity of a solution. In many equations, certain operations (like square roots, logarithms, or division) have restrictions on the input values. Ignoring these restrictions during the solution process can lead to the derivation of extraneous solutions, which must be eliminated upon verification.

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