Concursul GM, ziua 2, problema 1

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Laurentiu Tucaa
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Concursul GM, ziua 2, problema 1

Post by Laurentiu Tucaa »

Sa se rezolve in numere reale ecuatia \( \frac{x^3}{3}-x+\frac{\pi}{6}=arcctgx \)

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Last edited by Laurentiu Tucaa on Sat Sep 19, 2009 5:31 pm, edited 1 time in total.
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Theodor Munteanu
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Post 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 \( x=\sqrt 3 \).
La inceput a fost numarul. El este stapanul universului.
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