Question

Aflati x si y apartine lui Z pentru care avem egalitatiile a)x•y-3x+y=3 b)x•x+6x+5=0

Answer 1

$\it b)\ x\cdot x+6x+5=0 \Rightarrow x\cdot x+x+5x+5=0 \Rightarrow x(x+1)+5(x+1)=0 \Rightarrow\\ \\ \Rightarrow (x+1)(x+5)=0 \Rightarrow \begin{cases}\it x+5=0 \Rightarrow x=-5\\ \\ \it x+1=0 \Rightarrow x=-1\end{cases}$

$\it a)\ x\cdot y-3x+y=3 \Rightarrow x\cdot y-3x+y-3=0 \Rightarrow x(y-3)+(y-3)=0 \Rightarrow$

$\it \Rightarrow (y-3)(x+1)=0 \Rightarrow \begin{cases}\it x+1=0 \Rightarrow x=-1 \\ \\ \it y-3=0 \Rightarrow y=3 \end{cases}$