Question

Determina numerele naturale x,y astfel incat : (x-3)•(y+2)=12

Answer 1

$\rm y+2 \ \textgreater \ 0~si~12\ \textgreater \ 0 \Rightarrow x-3\ \textgreater \ 0 \Rightarrow x\ \textgreater \ 3. \\ (x-3) \in D_{12}= \{1;2;3;4;6;12\}.$

$\rm x-3=1 \Rightarrow x=4 \Rightarrow y+2=12 \Rightarrow y=10. \\ x-3=2 \Rightarrow x=5 \Rightarrow y+2=6 \Rightarrow y=4. \\ x-3=3 \Rightarrow x=6 \Rightarrow y+2=4 \Rightarrow y=2. \\ x-3=4 \Rightarrow x=7 \Rightarrow y+2=3 \Rightarrow y=1. \\ x-3=6 \Rightarrow x=9 \Rightarrow y+2=2 \Rightarrow y=0. \\ x-3=12 \Rightarrow x=15 \Rightarrow y+2=1,~nu~convine. \\ \\ Solutie: (x,y) \in \{(4,10);(5,4);(6,2);(7,1);(9,0)\}.$

Answer 2

(x-3)(y+2)=1*12=12*1=2*6=6*2=3*4=4*3
1)... x-3=1  ⇒ x=4   si  y+2=12⇒y=10;
2)... x-3=12⇒ x=15 si  y+2=1  ⇒y∉N;
3)... x-3=2  ⇒ x=5   si  y+2=6  ⇒y=4;
4)... x-3=6  ⇒ x=9   si  y+2=2  ⇒y=0;
5)... x-3=3  ⇒ x=6   si  y+2=4  ⇒y=2;
6)... x-3=4  ⇒ x=7   si  y+2=3  ⇒y=1;