CONCURS #016
24.02.2022, ora 20:00Problema 1 [286 puncte]
$Aflati\ suma\ primelor\ 5\ zecimale\ ale\ numarului\ \sqrt{2022}.$
Problema 2 [372 puncte]
$Cate\ numere\ intregi\ sunt\ in\ intervalul\ [-23,37]?$
Problema 3 [458 puncte]
$Un\ cub\ are\ volumul\ 216.\ Aflati\ aria\ totala. $
Problema 4 [544 puncte]
$Aflati\ produsul\ solutiilor\ ecuatiei\ |3x-1|=37.$
Problema 5 [630 puncte]
$Daca\ x^{2}-y^{2}=264,\ x+y=22,\ x,y\in \mathbb{N},\ calculati\ x\cdot y.$
Problema 6 [716 puncte]
$Aflati\ valoarea\ minima\ a\ expresiei\ E(a,b,c)=\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b},\ unde\ a,b,c>0,\ reale.$
Problema 7 [802 puncte]
$Cate\ numere\ naturale\ n\ exista\ astfel\ incat\ \sqrt{n+\sqrt{n+625}}\in \mathbb{N}?$
Problema 8 [888 puncte]
$Calculati\ suma\ S = 1\cdot 2+2\cdot 3+3\cdot 4+...+99\cdot 100.$