Question

Tìm `x;y``in`\(Z\) biết :

`a, x/3 + 1/y = 2/3`

`b, 1/x - 1/4 = y/2`

Answer 1

a) \(\dfrac{x}{3}+\dfrac{1}{y}=\dfrac{2}{3}\)

\(\Rightarrow xy+3=2y\left(y\ne0\right)\)

\(\Rightarrow y\left(x-2\right)=-3\)

\(\Rightarrow x-2;y\in U\left(3\right)=\left\{-1;1;-3;3\right\}\)

\(\Rightarrow\left(x;y\right)=\left(1;3\right);\left(3;-3\right);\left(-1;1\right);\left(5;-1\right)\)

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

\(\Rightarrow4-x=2xy\left(x\ne0\right)\)

\(\Rightarrow x\left(2y+1\right)=4\)

\(\Rightarrow x;\left(2y+1\right)\in U\left(4\right)=\left\{-1;1;-2;2;-4;4\right\}\)

\(\Rightarrow\left(x;y\right)=\left(4;0\right);\left(-4;-1\right)\)