Câu hỏi của Trần Khởi My

Question

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

Nguyen · Accepted Answer

$\Leftrightarrow2xy+3x-5y-11=0$

$\Leftrightarrow x\left(2y+3\right)=5y+11$

$\Rightarrow x=\frac{5y+11}{2y+3}=2+\frac{y+5}{2y+3}$

Để x nguyên thì $y+5⋮2y+3$

$\Rightarrow2y+10⋮2y+3$

$\Rightarrow7⋮2y+3$$\Rightarrow2y+3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}$

$\Rightarrow y\in\left\{-5;-2;-1;2\right\}$

$\Rightarrow x\in\left\{2;-1;6;3\right\}$

Vậy (x;y)=$\left(2;-5\right);\left(-1;-2\right);\left(6;-1\right);\left(3;2\right)$Câu trả lời: $\Leftrightarrow2xy+3x-5y-11=0$

$\Leftrightarrow x\left(2y+3\right)=5y+11$

$\Rightarrow x=\frac{5y+11}{2y+3}=2+\frac{y+5}{2y+3}$

Để x nguyên thì $y+5⋮2y+3$

$\Rightarrow2y+10⋮2y+3$

$\Rightarrow7⋮2y+3$$\Rightarrow2y+3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}$

$\Rightarrow y\in\left\{-5;-2;-1;2\right\}$

$\Rightarrow x\in\left\{2;-1;6;3\right\}$

Vậy (x;y)=$\left(2;-5\right);\left(-1;-2\right);\left(6;-1\right);\left(3;2\right)$

Lê Anh Duy · Answer

2xy -11 = 5y - 3x

=> 4xy - 22 - 10y+6x=0

$\Rightarrow2x\left(2x+3\right)-5\left(2y+3\right)-7=0$

$\Rightarrow\left(2x-5\right)\left(2y+3\right)=7$

Bảng

2x-5
			1    
			-1    
			7    
			-7

2y+3
			7
			-7
			1
			-1

x
			3
			2
			6
			-1

y
			2
			-5
			-1
			-2

Vây.....Câu trả lời: 2xy -11 = 5y - 3x