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Reference.org
Extraneous and missing solutions
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, 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. Both situations frequently result from performing operations that are not <a href="/facts/Inverse_function/Tg5nnXlu">invertible</a> for some or all values of the variables involved, which prevents the chain of logical implications from being bidirectional. </p>