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Extraneous solution

from class:

Algebra and Trigonometry

Definition

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation. These solutions often arise when manipulating equations, such as squaring both sides or taking logarithms.

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5 Must Know Facts For Your Next Test

  1. Extraneous solutions often appear when both sides of an equation are squared.
  2. Logarithmic and exponential equations can produce extraneous solutions due to domain restrictions.
  3. Always check potential solutions by substituting them back into the original equation.
  4. Extraneous solutions do not satisfy the initial conditions or constraints of the problem.
  5. When solving equations involving absolute values, logarithms, or radicals, carefully verifying each step is essential.

Review Questions

  • What is an extraneous solution and how does it arise?
  • Why is it important to check potential solutions in the original equation?
  • How can domain restrictions in logarithmic functions lead to extraneous solutions?

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