Question

a ) 32xy divizibil cu 45 , aflati x,y . b) 6x7 divizibil cu 49

Answer 1

$a)~\overline{32xy}-divizibil~cu~45 \Rightarrow \overline{32xy}-divizibil~cu~5~si~cu~9. \\ \\ \overline{32xy}-divizibil~cu~5 \Rightarrow y \in \{0;5\}. \\ \overline{32xy}-divizibil~cu~9 \Rightarrow 3+2+x+y=5+x+y~-divizibil~cu~9. \\ \\ \underline{Cazul~I}:~y=0~\Rightarrow 5+x -divizibil~cu~9 \Rightarrow x =4. \\ \underline{Cazul~II}:~y=5 \Rightarrow 10+x-divizibil~cu~9~\Rightarrow x=8. \\ \\ \underline{Solutie}: \boxed{\overline{32xy} \in \{3240;~3285\}}.$

$b) ~....................\\~~~~ 49*10=490 \\ ~~~~49*11=539 \\ ~~~~49*12=588 \\ ~~~~\boxed{49*13=637 } \\ ~~~~49*14=686 \\ ~~~~49*15=735 \\ ~~~~..................... \\ \\ Deci~numarul~este~637.$