Câu hỏi của Phương Linh

Question

1. Tìm x,y thuộc Z biết 2xy - x + y - 2 = 0

Đinh Đức Hùng · Accepted Answer

$2xy-x+y-2=0$$\Leftrightarrow4xy-2x+2y-4=0$$\Leftrightarrow2x\left(2y-1\right)+\left(2y-1\right)-3=0$$\Leftrightarrow\left(2x+1\right)\left(2y-1\right)=3$$\Rightarrow\left(2x+1\right)\left(2y-1\right)=1.3=3.1=\left(-1\right)\left(-3\right)=\left(-3\right)\left(-1\right)$Nếu $2x+1=1$ thì $2y-1=3$ $\Rightarrow x=0$ thì $y=2$Nếu $2x+1=3$ thì $2y-1=1$  $\Rightarrow x=1$ thì y = $1$Nếu $2x+1=-1$ thì $2y-1=-3$ $\Rightarrow x=-1$ thì $y=-1$Nếu $2x+1=-3$ thì $2y-1=-1$ $\Rightarrow x=-2$ thì y = $0$Vậy $\left(x;y\right)=\left(-2;0\right);\left(-1;-1\right);\left(0;2\right);\left(1;1\right)$Câu trả lời: $2xy-x+y-2=0$$\Leftrightarrow4xy-2x+2y-4=0$$\Leftrightarrow2x\left(2y-1\right)+\left(2y-1\right)-3=0$$\Leftrightarrow\left(2x+1\right)\left(2y-1\right)=3$$\Rightarrow\left(2x+1\right)\left(2y-1\right)=1.3=3.1=\left(-1\right)\left(-3\right)=\left(-3\right)\left(-1\right)$Nếu $2x+1=1$ thì $2y-1=3$ $\Rightarrow x=0$ thì $y=2$Nếu $2x+1=3$ thì $2y-1=1$  $\Rightarrow x=1$ thì y = $1$Nếu $2x+1=-1$ thì $2y-1=-3$ $\Rightarrow x=-1$ thì $y=-1$Nếu $2x+1=-3$ thì $2y-1=-1$ $\Rightarrow x=-2$ thì y = $0$Vậy $\left(x;y\right)=\left(-2;0\right);\left(-1;-1\right);\left(0;2\right);\left(1;1\right)$

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