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Concursul GM, ziua 2, problema 1
Posted: Wed Aug 19, 2009 2:29 pm
by Laurentiu Tucaa
Sa se rezolve in numere reale ecuatia \( \frac{x^3}{3}-x+\frac{\pi}{6}=arcctgx \)
Aurel Dobosan
Posted: Fri Aug 21, 2009 10:22 pm
by Theodor Munteanu
Ecuatia se reduce la \( \frac{{x^3 }}{3} - x + arctgx = \frac{\pi }{3} \) iar membrul stang e o functie strict crescatoare (semnul derivatei), deci ecuatia are solutie unica \( x=\sqrt 3 \).