$\text{Tổng hiệu tích tỉ lệ nghịch với} 35,210,12$
⇒$x+y:x-y:xy=\dfrac{1}{35}:\dfrac{1}{210}:\dfrac{1}{12}$
⇒$\dfrac{x+y}{\dfrac{1}{35}}=\dfrac{x-y}{\dfrac{1}{210}}=\dfrac{xy}{\dfrac{1}{12}}$
⇒$35(x+y)=210(x-y)=12xy$
⇒$\begin{cases}35(x+y)=210(x-y)\\210(x-y)=12xy\end{cases}$
⇒$\begin{cases}x-y=\dfrac{35(x+y)}{210}=\dfrac{x+y}{6}\\x-y=\dfrac{2xy}{35}\end{cases}$
⇒$\dfrac{x-y}{1}=\dfrac{x+y}{6}=\dfrac{x-y+x+y}{7}=\dfrac{2x}{7}=\dfrac{x+y-x+y}{5}=\dfrac{2y}{5}$
$\text{ Tính chất dãy tỉ số bằng nhau}$
⇒$x-y=\dfrac{2x}{7}=\dfrac{2xy}{35}$
⇒$y=5$
$x-y=\dfrac{2y}{5}=\dfrac{2xy}{35}$
⇒$x=7$
