Câu hỏi của _ Yuki _ Dễ thương _

Question

Số cặp (x;y) nguyên thỏa mãn $\frac{x}{6}-\frac{1}{y}=\frac{1}{2}$

Hoàng Thị Ngọc Anh · Accepted Answer

Ta có: $\frac{x}{6}-\frac{1}{y}=\frac{1}{2}$

$\Rightarrow\frac{1}{y}=\frac{1}{2}+\frac{x}{6}$

$\Rightarrow\frac{1}{y}=\frac{3+x}{6}$

$\Rightarrow\left(3+x\right)y=6$

$\Rightarrow3+x\inƯ\left(6\right);y\inƯ\left(6\right)$

mà $Ư\left(6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}$

$\Rightarrow3+x,y\in\left\{\pm1;\pm2;\pm3;\pm6\right\}$

$3+x$
			$1$
			$-1$
			2
			$-2$
			3
			$-3$
			$6$
			$-6$

$y$
			6
			$-6$
			3
			$-3$
			2
			$-2$
			1
			$-1$

$x$
			$-2$
			$-4$
			$-1$
			$-5$
			0
			$-6$
			3
			$-9$

Vậy $\left(x,y\right)\in\left\{\left(-4,-6\right);\left(-2,6\right);\left(-1,3\right);\left(-5,-3\right);\left(0,2\right);\left(-6,-2\right);\left(3,1\right);\left(-9,-1\right)\right\}$Câu trả lời: Ta có: $\frac{x}{6}-\frac{1}{y}=\frac{1}{2}$