Keyword Analysis & Research: extraneous solution definition

khanacademy.org

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:eq/x2ec2f6f830c9fb89:extraneous-sol/v/extraneous-solutions

WEBExtraneous solutions are values that we get when solving equations that aren't really solutions to the equation. In this video, we explain how and why we get extraneous solutions, by understanding the logic behind the process of solving equations.

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jdmeducational.com

https://jdmeducational.com/what-is-an-extraneous-solution-3-key-concepts-to-know/

WEBAn extraneous solution for an equation is a value we find when solving the equation that does not satisfy the equation. For example, if we square both sides of the equation √x = -1, we get a result of x = 1, which does not satisfy the original equation, which means x = 1 is an extraneous solution.

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varsitytutors.com

https://www.varsitytutors.com/hotmath/hotmath_help/topics/extraneous-solutions

WEBExtraneous Solutions. An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation. Example 1: Solve for x , 1 x − 2 + 1 x + 2 = 4 ( x − 2 ) ( x + 2 ) . 1 x − 2 + 1 x + 2 = 4 ( x − 2 ) ( x + 2 )

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socratic.org

https://socratic.org/precalculus/solving-rational-equations/extraneous-solutions

WEBKey Questions. How do I check for extraneous solutions? A lot of times in algebra, especially when you deal with radical functions, you will end up with what you call extraneous solutions. These are solutions to an equation that you will get as a result of your algebra, but are still not correct.

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wikipedia.org

https://en.wikipedia.org/wiki/Extraneous_and_missing_solutions

WEBIn mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. A missing solution is a valid one which is lost during the solution process.

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mathwords.com

http://www.mathwords.com/e/extraneous_solution.htm

WEBA solution of a simplified version of an equation that does not satisfy the original equation. Watch out for extraneous solutions when solving equations with a variable in the denominator of a rational expression, with a variable in the argument of a logarithm, or a variable as the radicand in an nth root when n is an even number. --- definition

definition

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khanacademy.org

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:eq/x2ec2f6f830c9fb89:extraneous-sol/a/analyzing-extraneous-solutions-of-square-root-equations

WEBExtraneous solutions are not necessarily outside the domain. But they can appear as extra solutions when we square both sides of an equation, because when we square an equation, we would get the same result whether the original equation was positive or …

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media4math.com

https://www.media4math.com/library/definition-rationals-and-radicals-extraneous-solution

WEBExtraneous Solutions. Solving equations is an important skill, but sometimes you end up finding more solutions than you realize. Watch the following video to learn how to identify extraneous solutions when they occur. (The transcript is also included.)

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youtube.com

https://www.youtube.com/watch?v=Hz3vkU3gTeI

WEBKeep going! Check out the next lesson and practice what you’re learning:https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:eq/x2ec2f6f830c9fb89:extr...

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libretexts.org

https://math.libretexts.org/Courses/Long_Beach_City_College/Book%3A_Intermediate_Algebra/Text/08%3A_Rational_Expressions_and_Equations/8.6%3A_Solve_Rational_Equations

WEBAn extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined. We note any possible extraneous solutions, c, by writing x ≠ c x ≠ c next to the equation. How to Solve Equations with Rational Expressions.

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