Extraneous and missing solutions

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SUMMARY

This discussion centers on the challenges of identifying and eliminating extraneous solutions in mathematical equations. Participants emphasize the importance of examining the original equations to identify values that may not be valid solutions, rather than solely relying on substitution methods. The conversation highlights that while this approach is effective in intermediate algebra and Pre-Calculus, its applicability in post-calculus mathematics may not be as straightforward. The consensus is that a thorough understanding of the original equations is crucial for accurate solution identification.

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  • Intermediate Algebra concepts
  • Pre-Calculus problem-solving techniques
  • Understanding of extraneous solutions in equations
  • Basic knowledge of mathematical equations and their properties
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  • Research methods for identifying extraneous solutions in algebraic equations
  • Explore advanced techniques in calculus for solution verification
  • Study the implications of extraneous solutions in higher-level mathematics
  • Learn about the role of original equations in determining valid solutions
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Mathematics students, educators, and anyone involved in solving equations who seeks to improve their understanding of extraneous and missing solutions.

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While solving equations, most would have at some point or another had to deal with the annoyance of extraneous or missing solutions.
While I have vigorously taught myself over the years how to avoid losing solutions, gaining extra solutions is still and will probably always be inevitable for me (in order to keep things simple).

I'm curious to know if extraneous solutions can be found and eliminated in a set of solutions by means other than substituting and checking in the original equation.
 
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Mentallic, the best way is to examine the original equation or origianal set of equations. Examine those for values which will not work or need to be excluded. Is your viewpoint that of intermediate algebra and Pre-Calculus?
 
I agree examining the equation would also suffice, but this is sometimes not so obvious, which would again lead to simple plug-and-check.

Yes my viewpoint is just that, but does this mean the rules don't apply so bluntly for post-calculus mathematics?
 

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