Talk:Extraneous and missing solutions: Difference between revisions

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{{Maths rating|class=start|importance=low|field=algebra}}

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==First Example==

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If you search '''extraneous solution''' in Yahoo!, you can find many topics talking about '''extraneous solution'''. http://www.jcoffman.com/Algebra2/ch1_5.htm and http://www.mathpath.org/proof/argument.invalid.htm are two appropriate examples.[[User:Doraemonpaul|Doraemonpaul]] ([[User talk:Doraemonpaul|talk]]) 19:51, 18 February 2009 (UTC)

Neither 7 nor -4 satisfy the equation -- regardless of what our domains are. Just plug them into the equation. Do the math and you will see too.

Also, I think it was great that you explained how a solution is not considered extraneous if it only does not satisfy the manually-formed ___domain (as opposed to the naturally-formed ___domain).

The word is "satisfy," by the way -- not "satisfly." [[User:MusicHuman|MusicHuman]] ([[User talk:MusicHuman|talk]]) 14:52, 17 December 2022 (UTC)

== My changes ==

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There is another type of extraneous solution, that is not mentioned in the article. A solution to an equation arising from an applied problem may be considered extraneous if it is not physically meaningful. A negative length could be an example of this. See http://mathcentral.uregina.ca/QQ/database/QQ.09.02/paul2.html [[Special:Contributions/66.41.7.193|66.41.7.193]] ([[User talk:66.41.7.193|talk]]) 05:00, 29 March 2008 (UTC)

== Example with the imaginary unit, ''i'' ==

Is this a useful example? It got me confused for a while just now:

We know that <math>\frac{1}{i}=-i</math>. However,

<math>\frac{1}{i}=i^{-1}=((-1)^{\frac{1}{2}})^{-1}=\sqrt{(-1)^{-1}}=\pm i</math>

But only <math>-i</math> satisfies the original equation, <math>+i</math> is an extraneous solution.

--[[User:MTres19|MTres19]] ([[User talk:MTres19|talk]]) 19:38, 29 April 2020 (UTC)