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When Close Enough Is Close Enough

Zhe Hu
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The following equation is taken from my brother's algebra workbook. Sqrt(5-2*Sqrt(6))=Sqrt(3)-Sqrt(2)

He always challenges me to prove these equations like this by Mathematica, otherwise to remove this software to save disk space for his PC games. I am very lucky that Mathematica's FullSimplify[] function is powerful enough to solve these problems. But I am not sure whether what my brother brings next time may prove Mathematica a "failure."

After reading Edward R. Scheinerman's article "When Close Enough Is Close Enough" published on American Math Monthly June-July 2000, I know how to check equality "manually" if FullSimplify happens to fail. I implement a function according to Scheinerman's theory. In this Notebook, CalculateEquality[] is such a function. You can check the equality of algrebraic integers (roots of some monic, integer polynomial) by numerical calculation.

*Wolfram Technology > Programming > Equation Solving

implementing functions, FullSimplify
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*When Close Enough is Close Enough   [in Articles]
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ReadMe.txt (826 B) - ASCII-Text
Close.nb (25 KB) - Mathematica Notebook