**Extraneous and missing solutions - Wikipedia**
https://en.wikipedia.org/wiki/Extraneous_and_missing_solutions

In mathematics, an extraneous solution is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem. A missing solution is a solution that is a valid solution to the problem, but disappeared during the process of solving the problem. Both are frequently the consequence of performing operations that are not invertible for some or all values of the variables, which prevents the chain of logical implications in the proof

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