\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\)
\(\Leftrightarrow\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{1}{5}\)
\(\Leftrightarrow\dfrac{x+y}{xy}=\dfrac{1}{5}\)
\(\Leftrightarrow5\left(x+y\right)=xy\)
sao nx nhỉ
Quy đồng lên, ta có :5x+5y=xy
\(\rightarrow\) x (5-y) = -5y
\(\rightarrow\)
\(\rightarrow\)
\(\rightarrow\)
\(\rightarrow\)
x nguyên \(\rightarrow\dfrac{-25}{5-y}\) nguyên \(\rightarrow\) 5-y \(\in\) Ư(25)
Ư(25)={-25,-5,-1,1,5,25}
\(\Rightarrow\)y lần lượt là :-30,-10,-6,-4,20 và x lần lượt là :6,10,30,-20,4
\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\Rightarrow\dfrac{5y}{5xy}+\dfrac{5x}{5xy}=\dfrac{xy}{5xy}\)
\(\Rightarrow xy-5x-5y+25=25\)
\(\Rightarrow x\left(y-5\right)-5\left(y-5\right)=25\)
\(\Rightarrow\left(x-5\right)\left(y-5\right)=25\)
| x-5 | 1 | -1 | 5 | -5 | 25 | -25 | |||
| y-5 | 25 | -25 | 5 | -5 | 1 | -1 | |||
| x | 6 | 4 | 10 | L | 30 | -20 | |||
| y | 30 | -20 | 10 | L | 6 | 4 |
