Question

Tìm x, y ϵ Z.

 \(\dfrac{4}{x}-\dfrac{y}{2}=\dfrac{1}{4}\)

 

 

Answer 1

\(\dfrac{4}{x}-\dfrac{y}{2}=\dfrac{1}{4}\Leftrightarrow\dfrac{8-xy}{2x}=\dfrac{1}{4}\Leftrightarrow\dfrac{16-2xy}{4x}=\dfrac{x}{4x}\)

\(\Rightarrow16-2xy=x\Leftrightarrow x+2xy=16\Leftrightarrow x\left(1+2y\right)=16\)

\(\Rightarrow x;1+2y\inƯ\left(16\right)=\left\{\pm1;\pm2;\pm4;\pm8;\pm16\right\}\)

x	1	-1	2	-2	4	-4	8	-8	16	-16
2y + 1	16	-16	8	-8	4	-4	2	-2	1	-1
y	15/2 ( ktm )	-17/2 ( ktm )	7/2 ( ktm )	-9/2 ( ktm )	3/2 ( ktm )	-5/2 ( ktm )	1/2 ( ktm )	-3 / 2 ( ktm )	0	-1