Question

\(\dfrac{1}{x}\)+\(\dfrac{y}{3}\)=\(\dfrac{5}{6}\)

câu này x,y ϵ {(-6,3};(6,2);(-2,4);(2,1}

đ chx

Answer 1

`1/x + y/3 = 5/6`

`-> 1/x = 5/6 - y/3`

`-> 1/x = 5/6 - ( 2y ) / 6`

`-> 1/x = ( 5 - 2y ) / 6`

`-> x ( 5 - 2y ) = 6`

Answer 2

Answer 3

\(x,y\in Z\)

\(\dfrac{1}{x}+\dfrac{y}{3}=\dfrac{5}{6}\left(x\ne0\right)\)

\(\Rightarrow\dfrac{6}{6x}+\dfrac{2xy}{6x}=\dfrac{5x}{6x}\)

\(\Rightarrow6+2xy=5x\)

\(\Rightarrow5x-2xy=6\)

\(\Rightarrow x\left(5-2y\right)=6\)

\(\Rightarrow x=\dfrac{6}{5-2y}\left(y\ne\dfrac{5}{2}\right)\)

Vì x,y là các số nguyên nên:

\(6⋮\left(5-2y\right)\)

\(\Rightarrow5-2y\inƯ\left(6\right)\)

\(\Rightarrow5-2y\in\left\{1;2;3;6;-1;-2;-3;-6\right\}\)

\(\Rightarrow y\in\left\{2;1;3;4\right\}\)

*\(y=2\text{​​}\Rightarrow x=\dfrac{6}{5-2.2}=6\left(n\right)\)

\(y=1\text{​​}\Rightarrow x=\dfrac{6}{5-2.1}=2\left(n\right)\)

\(y=3\text{​​}\Rightarrow x=\dfrac{6}{5-2.3}=-6\left(n\right)\)

\(y=4\text{​​}\Rightarrow x=\dfrac{6}{5-2.4}=-2\left(n\right)\)

Vậy các cặp số x,y nguyên thỏa mãn (phương trình) là (6,2) ; (2,1) ; (-6,3) ; (-2,4).