When and why extraneous solution happen | Summary and Q&A

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July 19, 2019
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Khan Academy
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When and why extraneous solution happen

TL;DR

Learn about extraneous solutions in algebraic equations and the reasons behind their occurrence.

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Questions & Answers

Q: What are extraneous solutions in algebraic equations?

Extraneous solutions refer to solutions that do not satisfy the original equation, often occurring in radical and rational equations due to irreversible algebraic operations.

Q: Why are extraneous solutions more common in radical and rational equations?

These equations involve operations like squaring and multiplying both sides of the equation, which are not reversible and can introduce extraneous solutions.

Q: What should be done when encountering extraneous solutions?

After solving an equation, substitute the values of the solutions back into the original equation to check if they satisfy it. If any solution does not work, it is considered extraneous.

Q: What are some common algebraic operations that can lead to extraneous solutions?

Squaring both sides of an equation and multiplying both sides by a variable or an expression involving a variable are two operations that can introduce extraneous solutions.

Summary & Key Takeaways

  • Extraneous solutions are solutions that do not work in the original equation, often occurring in radical and rational equations.

  • Algebraic manipulation operations like squaring and multiplying both sides of an equation by a variable are not reversible, leading to extraneous solutions.

  • It is crucial to check for extraneous solutions when solving equations, especially in radical and rational equations.

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