CONCURS #024
17.03.2022, ora 20:00Problema 1 [263 puncte]
$Daca\ |x-36|+|x-49|=0,\ aflati\ media\ geometrica\ a\ numerelor\ x\ si\ y.$
Problema 2 [326 puncte]
$Daca\ a^{2}-b^{2}=84\ si\ a-b=7,\ aflati\ valoarea\ lui\ a.$
Problema 3 [389 puncte]
$Suma\ a\ patru\ numere\ naturale\ nenule\ este\ 2024.\ Care\ este\ cea\ mai\ mica\ valoare\ posibila$
$a\ celui\ mai\ mic\ multiplu\ comun\ al\ lor?$
Problema 4 [452 puncte]
$Fie\ multimea\ A=\{ 1,2,3,...,15 \}. Cate\ submultimi\ nevide\ ale\ lui\ A\ au\ produsul$
$elementelor\ un\ numar\ prim\ cu\ 210? $
Problema 5 [515 puncte]
$Daca\ \sqrt{\overline{abc}}+\sqrt{\overline{bc}}=30,\ aflati\ numarul\ \overline{bac}.$
Problema 6 [578 puncte]
$Determinati\ N\ natural\ minim\ astfel\ incat\ 144\cdot N\ are\ 35\ divizori.$
Problema 7 [641 puncte]
$Daca\ x\cdot (x-2)=2022\ si\ y\cdot (y-2)=2022,\ iar\ x\ si\ y\ distincte,\ calculati\ x^{2}+y^{2}.$
Problema 8 [704 puncte]
$Cate\ solutii\ are\ ecuatia\ |x-1|+|y-1|+|z-1|+|w-1|=2,\ unde\ x,y,z,w\in \mathbb{Z}?$