Question

Tìm x , y ϵ Z biết :

\(a,\frac{1}{x}=\frac{1}{6}+\frac{y}{3}\)

\(b,\frac{x}{6}-\frac{1}{y}=\frac{1}{2}\)

Answer 1

a)\(\frac{1}{x}=\frac{1}{6}+\frac{y}{3}\)

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

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

\(\Rightarrow x\left(2y+1\right)=6\)

\(\Rightarrow x;2y+1\inƯ\left(6\right)=\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

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Answer 2

b)\(\frac{x}{6}-\frac{1}{y}=\frac{1}{2}\)

\(\Rightarrow\frac{xy}{6y}-\frac{6}{6y}=\frac{1}{2}\)

\(\Rightarrow\frac{xy-6}{6y}=\frac{1}{2}\)

\(\Rightarrow2\left(xy-6\right)=6y\)

\(\Rightarrow2xy-12-6y=0\)

\(\Rightarrow2\left(xy-3y-6\right)=0\)

\(\Rightarrow xy-3y-6=0\)

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