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Extraneous Solutions - GeeksforGeeks Extraneous solutions often arise when the steps to solve the equation involve squaring both sides, multiplying by expressions that could be zero, or other manipulations that might introduce solutions not valid in the original context
Extraneous and missing solutions - Wikipedia In general, whenever we multiply both sides of an equation by an expression involving variables, we introduce extraneous solutions wherever that expression is equal to zero But it is not sufficient to exclude these values, because they may have been legitimate solutions to the original equation
What is an extraneous solution? Select all that apply: When solving, you may end up with solutions that don't hold true when substituted back, classifying them as extraneous solutions To identify and verify if a solution is extraneous, always plug the solution back into the original equation If it does not satisfy the equation, then it is indeed extraneous Thus, based on your answer options:
Extraneous Solutions Definition - Intermediate Algebra Key Term | Fiveable Extraneous solutions are solutions to an equation that do not satisfy the original equation They are not valid solutions, as they are introduced during the process of solving the equation, often through algebraic manipulations
Extraneous Solutions Definition - Honors Algebra II Key Term | Fiveable Extraneous solutions are solutions that arise from the process of solving an equation but do not satisfy the original equation They often occur in equations that involve rational expressions or square roots, where certain manipulations can introduce these false solutions
Extraneous Variables | Examples, Types Controls - Scribbr In an experiment, an extraneous variable is any variable that you’re not investigating that can potentially affect the outcomes of your research study If left uncontrolled, extraneous variables can lead to inaccurate conclusions about the relationship between independent and dependent variables
Extraneous Solutions | Precalculus - Lumen Learning We have to be careful when solving radical equations as it is not unusual to find extraneous solutions, roots that are not, in fact, solutions to the equation These solutions are not due to a mistake in the solving method, but result from the process of raising both sides of an equation to a power
Understanding Extraneous Solutions in Mathematics Extraneous solutions are false answers that appear during the process of solving an equation They show up because of the steps we take to manipulate the equation Even though they seem valid while solving, they won’t satisfy the original equation when you plug them back in
Solving Equations: Extraneous Solutions An extraneous solution is the solution of the simplified form of an equation that does not satisfy the original equation and needs to be eliminated It is necessary to check for extraneous solutions when the original equation has a restricted domain
Common Types of Mistakes: Extraneous Solutions Sometimes a method used to solve an equation gives extraneous solutions - values which arise from the solution method but that are not solutions of the original equation