Pana la urma a rezolvat cineva problema asta? Am vazut-o, parca, postata la a VIIa sau la a VIIIa. M-ar interesa si pe mine o solutie, mai ales ca se apropie olimpiada!
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Emergency stop.
O metoda de rezolvare ar putea fi :
Pornind de la formula radicalilor compusi adica SQRT(a+SQRT(b) ) = SQRT ((a+SQRT(a^2 -b))/2) + SQRT ((a – SQRT(a^2 -b))/2)
Inlocuim a=x^2 +x+1 si b=2x^3 + x^2 + 2x , prelucram si obtinem x=0 solutie unica
Multumesc mult, Bedrix.
*** QuickLaTeX cannot compile formula: \[\begin{array}{l} {\rm{Rezolvati in multimea numerelor reale ecuatia] *** Error message: \begin{array} on input line 9 ended by \end{document}. leading text: \end{document} Improper \prevdepth. leading text: \end{document} Missing $ inserted. leading text: \end{document} Missing } inserted. leading text: \end{document} Missing } inserted. leading text: \end{document} Missing } inserted. leading text: \end{document} Missing \cr inserted. leading text: \end{document} Missing $ inserted. leading text: \end{document} You can't use `\end' in internal vertical mode. leading text: \end{document} \begin{array} on input line 9 ended by \end{document}. leading text: \end{document} Missing } inserted. leading text: \end{document} Emergency stop.Ai complicat. Nu este necesara ridicarea la patrat , trebuie prelucrat a^2-b ; formula radicalilor compusi se aplica daca a^2-b este p.p.
Am incercat sa-l „prelucrez” dar mai rau m-am incurcat!!!
![\[{\rm{Verificam daca }}{a^2} - b{\rm{ este patrat perfect]](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-83873894744dd797bda298651c5739e3_l3.png "formula matematica")
Din ultima relatie ar rezulta ca x = 0 e singura solutie (daca calculele pina aici sunt corecte, n-am urmarit). Nu e suficient ??
(x^2+x+1)^2 -(2x^3+x^2+2x)=x^4 +x^2 +1+2x^3 +2x^2 +2x – 2x^3 -x^2 -2x =x^4 +2x^2 +1=(x^2 +1)^2
Din ce in ce mai simplu. Multumesc.
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L-am refacut. Multumesc.