Tuesday, 26 April 2016

algebra precalculus - Why does 2+2=5 in this example?





I stumbled across the following computation proving 2+2=5



calculation proving 2+2=5




Clearly it doesn't, but where is the mistake? I expect that it's a simple one, but I'm even simpler and don't really understand the application of the binomial form to this...


Answer



The error is in the step where the derivation goes from
(492)2=(592)2
to
(492)=(592)



In general, if a2=b2 it is not necessarily true that a=b; all you can conclude is that either a=b or a=b. In this case, the latter is true, because (492)=12 and (592)=12. Once you have written down the (false) equation 12=12 it is easy to derive any false conclusion you want.


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