Câu hỏi của Nguyễn Hoàng Giang

Question

Tìm các số nguyên x,y biết: x-2xy+y-3=0

Đinh Đức Hùng · Accepted Answer

$x-2xy+y-3=0$$\Leftrightarrow x-2xy+y=3$$\Leftrightarrow2x-4xy+2y=6$$\Leftrightarrow2x-2y\left(2x-1\right)=6$$\Leftrightarrow\left(2x-1\right)-2y\left(2x-1\right)=5$$\Leftrightarrow\left(2x-1\right)\left(1-2y\right)=5$$\Leftrightarrow\left(2x-1\right)\left(1-2y\right)=1.5=\left(-1\right)\left(-5\right)$Nếu $2x-1=1$ thì $1-2y=5$ $\Rightarrow x=1$ thì $y=-2$Nếu $2x-1=5$ thì $1-2y=1$ $\Rightarrow x=3$thì$y=0$Nếu $2x-1=-1$ thì $1-2y=-5$ $\Rightarrow x=0$thì$y=3$Nếu $2x-1=-5$ thì $1-2y=-1$ $\Rightarrow x=-2$thì$y=1$Vậy $\left(x;y\right)=\left(1;-2\right);\left(-2;1\right);\left(3;0\right);\left(0;3\right)$Câu trả lời: $x-2xy+y-3=0$$\Leftrightarrow x-2xy+y=3$$\Leftrightarrow2x-4xy+2y=6$$\Leftrightarrow2x-2y\left(2x-1\right)=6$$\Leftrightarrow\left(2x-1\right)-2y\left(2x-1\right)=5$$\Leftrightarrow\left(2x-1\right)\left(1-2y\right)=5$$\Leftrightarrow\left(2x-1\right)\left(1-2y\right)=1.5=\left(-1\right)\left(-5\right)$Nếu $2x-1=1$ thì $1-2y=5$ $\Rightarrow x=1$ thì $y=-2$Nếu $2x-1=5$ thì $1-2y=1$ $\Rightarrow x=3$thì$y=0$Nếu $2x-1=-1$ thì $1-2y=-5$ $\Rightarrow x=0$thì$y=3$Nếu $2x-1=-5$ thì $1-2y=-1$ $\Rightarrow x=-2$thì$y=1$Vậy $\left(x;y\right)=\left(1;-2\right);\left(-2;1\right);\left(3;0\right);\left(0;3\right)$

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