CONCURS #006
12-08-2022 17:04:52Problema 1 [296 puncte]
$Daca\ A=1+3+5+7+9+11+13,\ calculati\ radacina\ patrata\ a \ lui\ A.$
Problema 2 [392 puncte]
$ Calculati\ |\sqrt{7}-3|+|\sqrt{7}-2|.$
Problema 3 [488 puncte]
$Un\ dreptunghi\ are\ lungimea\ 12\ si\ diagonala\ 13.\ Aflati\ aria\ dreptunghiului.$
Problema 4 [584 puncte]
$Calculati\ partea\ intreaga\ a\ numarului\ \sqrt{333}.$
Problema 5 [680 puncte]
$Numerele\ a\ si\ b\ sunt\ rationale\ astfel\ incat:$
$(2\cdot a-13)\cdot \sqrt{2}+\frac{b-14}{\sqrt{2}+1}=0.\ Calculati\ a\cdot b.$
Problema 6 [776 puncte]
$Aflati\ numarul\ solutiilor\ ecuatiei:\ \ x\cdot y+x=6^{31},\ unde\ x,y\in \mathbb{N}.$
Problema 7 [872 puncte]
$O\ multime\ A\ are\ 120\ submultimi\ cu\ cate\ 3\ elemente.\ Aflati\ cate\ elemente\ are\ A.$
Problema 8 [968 puncte]
$Un\ trapez\ isoscel\ cu\ diagonalele\ perpendiculare\ are\ lungimea\ liniei\ mijlocii\ egala\ cu\ 12.$
$Calculati\ aria\ trapezului.$