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Asupra unor ecuatii exponentiale

 
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Cezar Lupu
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Joined: 26 Sep 2007
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Location: Pittsburgh/Craiova/Bucharest/Constanta

PostPosted: Wed Apr 16, 2008 1:30 am    Post subject: Asupra unor ecuatii exponentiale Reply with quote

In aceasta scurta nota vom discuta doua ecuatii exponentiale in numere strict pozitive care pot fi abordate pe metoda rezolvarii ecuatiei

x^y+y^x=1+xy

in numere strict pozitive.

Cele doua ecuatii abordate in nota sunt:

\left(\frac{x}{y}\right)^{x}+\left(\frac{y}{x}\right)^{y}=2

si \left(\frac{x}{y}\right)^{y}+\left(\frac{y}{x}\right)^{x}=2.

Desi sunt inrudite cele doua ecuatii au rezolvari diferite; prima fiind usoara pe cand ce-a de-a doua nu este chiar asa. De fapt un caz ramane deschis.
Pentru mai multe detalii, puteti consulta: Asupra unor ecuatii exponentiale.
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An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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