mateforum.ro Forum Index mateforum.ro

 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Ialomita , etapa judeteana

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a V-a
View previous topic :: View next topic  
Author Message
alex2008
Leibniz


Joined: 19 Oct 2008
Posts: 489
Location: Tulcea

PostPosted: Wed Nov 12, 2008 9:31 pm    Post subject: Ialomita , etapa judeteana Reply with quote

Sa se determine cifrele x, y si z, stiind ca : \frac{1}{x+2y+3z}=\overline{0,xy}.
Back to top
View user's profile Send private message
Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Wed Apr 08, 2009 3:15 pm    Post subject: Re:Ialomita , etapa judeteana Reply with quote

\frac{1}{x+2y+3z}=\overline{0,xy}\Rightarrow \frac{1}{x+2y+3z}=\frac{\overline{xy}}{100}\Rightarrow \overline{xy}(x+2y+3z)=100\Rightarrow \overline{xy} \in \{10, 20, 25, 50\}
Analizand pentru fiecare valoare a lui \overline{xy}, obtinem (x; y; z)\in \{(1; 0; 3); (2; 0; 1)\}.


Last edited by Andi Brojbeanu on Fri Jun 19, 2009 2:34 pm; edited 1 time in total
Back to top
View user's profile Send private message Send e-mail Yahoo Messenger
Claudiu Mindrila
Fermat


Joined: 01 Oct 2007
Posts: 557
Location: Targoviste

PostPosted: Wed Apr 08, 2009 4:48 pm    Post subject: Re:Ialomita , etapa judeteana Reply with quote

Andi Brojbeanu wrote:
1/(x+2y+3z) =0,xy rezulta 100=(10x+y)(x+2y+3z). Cei doi factori apartin {1;2;4;5;10;20;25;50;100}. Analizand fiecare caz in parte, obtinem solutia finala (x;y;z) apartine {(1;0;3);(2;0;1)}.


\frac{1}{x+2y+3z}=\overline{0,xy} \Longrightarrow (10x+y)(x+2y+3z)=100  \Longrightarrow    10x+y\in \mathcal{D}_{100} \wedge \ x+2y+3z\in \mathcal{D}_{100}. Analizand situatiile care apar obtinem ca \left(x,\ y,\ z\right)\in\left\{ \left(1,\ 0,\ 3\right),\ \left(2,\ 0,\ 1\right)\right\}
_________________
elev, clasa a XI-a, C. N. "C-tin Carabella", Targoviste
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Display posts from previous:   
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a V-a All times are GMT + 2 Hours
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum



Powered by phpBB © 2001, 2005 phpBB Group