Question

[Nguyễn Gia Huy]

 Tìm các giá trị nguyên của  x và y biết: 5y – 3x = 2xy – 11.

Answer 1

[Nguyen An Ninh]

5y−3x=2xy−11 
\Rightarrow2xy+3x-5y-11=0⇒2xy+3x−5y−11=0 
\Rightarrow4xy+6x-10y-22=0⇒4xy+6x−10y−22=0 
\Rightarrow\left(4xy+6x\right)-\left(10y+15\right)=7⇒(4xy+6x)−(10y+15)=7 
\Rightarrow2x\left(2y+3\right)-5\left(2y+3\right)=7⇒2x(2y+3)−5(2y+3)=7 
\Rightarrow\left(2x-5\right)\left(2y+3\right)=7⇒(2x−5)(2y+3)=7 
Ta có các TH sau:
TH1: \left\{\begin{matrix}2x-5=1\\2y+3=7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=3\\y=2\end{matrix}\right.{2x−5=12y+3=7​⇒{x=3y=2​ 
TH2: \left\{\begin{matrix}2x-5=-1\\2y+3=-7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2\\y=-5\end{matrix}\right.{2x−5=−12y+3=−7​⇒{x=2y=−5​ 
TH3: \left\{\begin{matrix}2x-5=7\\2y+3=1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=6\\y=-1\end{matrix}\right.{2x−5=72y+3=1​⇒{x=6y=−1​ 
TH4: \left\{\begin{matrix}2x-5=-7\\2y+3=-1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=-1\\y=-2\end{matrix}\right.{2x−5=−72y+3=−1​⇒{x=−1y=−2​ 
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