CONCURS #015
23.02.2022, ora 20:00Problema 1 [291 puncte]
$Calculati\ E=\sqrt{2}\cdot (\sqrt{98}+\sqrt{32}-\sqrt{72}).$
Problema 2 [382 puncte]
$Calculati\ media\ geometrica\ a\ numerelor\ 588\ si\ 9075.$
Problema 3 [473 puncte]
$Un\ triunghi\ dreptunghic\ are\ catetele\ proportionale\ cu\ 5\ si\ 12,\ iar\ perimetrul\ este\ 210. $
$Aflati\ aria\ triunghiului.$
Problema 4 [564 puncte]
$Rezolvati\ ecuatia\ 3(x-29)=2(x+37).$
Problema 5 [655 puncte]
$Trapezul\ dreptunghic\ ABCD,\ cu\ AB||CD,\ are\ AB=29,\ CD=76,\ \widehat{C}=60^{0}.$
$Aflati\ lungimea\ lui\ BC.$
Problema 6 [746 puncte]
$Cate\ elemente\ rationale\ are\ sirul\ \sqrt{1}, \sqrt{2}, \sqrt{3},...,\sqrt{2379}?$
Problema 7 [837 puncte]
$Aflati\ cel\ mai\ mare\ numar\ natural\ n\ astfel\ incat\ \sqrt{n+\sqrt{n+29}}\in \mathbb{N}.$
Problema 8 [928 puncte]
$Daca\ 1^{3}+2^{3}+3^{3}+...+2022^{3}=n^{2},\ aflati\ n.$