An extraneous solution is a solution derived from an equation that is not valid within the original equation. Extraneous solutions often arise when both sides of an equation are manipulated.
5 Must Know Facts For Your Next Test
Extraneous solutions commonly occur when solving exponential and logarithmic equations, especially after squaring both sides or applying logarithms.
Identifying extraneous solutions involves substituting them back into the original equation to verify their validity.
Extraneous solutions can be introduced by operations that are not reversible, such as squaring both sides of an equation.
When working with logarithmic functions, ensuring the argument of the logarithm remains positive is crucial to avoid extraneous solutions.
In exams, students should always check for extraneous solutions as part of their final answer verification process.