\(\dfrac{5}{x}+\dfrac{y}{4}=\dfrac{1}{8}\Rightarrow\dfrac{5}{x}=\dfrac{1}{8}-\dfrac{y}{4}\)
\(\Rightarrow\dfrac{5}{x}=\dfrac{1}{8}-\dfrac{2y}{8}\Rightarrow\dfrac{5}{x}=\dfrac{1-2y}{8}\)
\(\Rightarrow x\left(1-2y\right)=5.8\Rightarrow x\left(1-2y\right)=40\)
... ( tự làm tiếp )
\(\dfrac{5}{x}+\dfrac{y}{4}=\dfrac{1}{8}\)
\(\Leftrightarrow\dfrac{5}{x}=\dfrac{1}{8}-\dfrac{y}{4}\)
\(\dfrac{5}{x}=\dfrac{1}{8}-\dfrac{2y}{8}\)
\(\dfrac{5}{x}=\dfrac{1-2y}{8}\)
\(\Leftrightarrow5.8=x\left(1-2y\right)\)
\(\Leftrightarrow40=x\left(1-2y\right)\)
\(\Leftrightarrow x;1-2y\inƯ\left(40\right)\)
\(Ư\left(\text{40}\right)=\left\{\pm1;\pm2;\pm4;\pm5;\pm8;\pm10;\pm20;\pm40\right\}\)
\(1-2y\)lẻ
\(\Leftrightarrow1-2y=1\Rightarrow0\Rightarrow y=0\)
\(x=40\)
\(\Leftrightarrow1-2y=-1\Rightarrow2y=2\Rightarrow y=1\)
\(x=-40\)
\(\Leftrightarrow1-2y=5\Rightarrow2y=-4\Rightarrow y=-2\)
\(x=8\)
\(\Leftrightarrow1-2y=-5\Rightarrow2y=6\Rightarrow y=3\)
\(x=-8\)
Ta có :
\(\dfrac{5}{x}+\dfrac{y}{4}=\dfrac{1}{8}\)
\(\Rightarrow\dfrac{1}{8}-\dfrac{5}{x}=\dfrac{y}{4}\)
\(\Rightarrow\dfrac{x}{8x}-\dfrac{40}{8x}=\dfrac{y}{4}\)
\(\Rightarrow\dfrac{40}{8x}=\dfrac{y}{4}\)
\(\Rightarrow8x.y=40.4\)
\(\Rightarrow8.x.y=160\)
\(\Rightarrow x.y=20=1.20=20.1=2.10=10.2=4.5=5.4=\left(-1\right).\left(-20\right)=\left(-20\right).\left(-1\right)=\left(-2\right).\left(-10\right)=\left(-10\right).\left(-2\right)=\left(-4\right).\left(-5\right)=\left(-5\right).\left(-4\right)\)Vậy cặp giá trị (x,y) cần tìm là :
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