Question

[Hatsume Miku]

Tìm số nguyên x và y,biết : xy - x + 2y = 3

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Answer 1

[Tung Duong]

xy−x+2y=3xy−x+2y=3

xy−x+2y−3=0xy−x+2y−3=0

xy−x+2y−3+1=1xy−x+2y−3+1=1

x(y−1)+2(y−1)=1x(y−1)+2(y−1)=1

(y−1).(x+2)=1(y−1).(x+2)=1

⇒[y−1=1;−1x+2=1;−1⇒[y−1=1;−1x+2=1;−1

⇒\(\orbr{\begin{cases}\\\end{cases}}\)y−1=1⇒y=1+1=2x+2=1⇒x=1−2=−1⇒[y−1=1⇒y=1+1=2x+2=1⇒x=1−2=−1

⇒\(\orbr{\begin{cases}\\\end{cases}}\)y−1=−1⇒y=−1+1=0x+2=−1⇒x=−1−2=−3⇒[y−1=−1⇒y=−1+1=0x+2=−1⇒x=−1−2=−3

Vậy y={2;0},x={−1;−3}

Answer 2

[Đặng Tú Phương]

\(xy-x+2y=3\)

\(\Rightarrow x\left(y-1\right)+2y-2=2+3\)

\(\Rightarrow x\left(y-1\right)+2\left(y-1\right)=5\)

\(\Rightarrow\left(x+2\right)\left(y-1\right)=5\)

Vì x;y thuộc Z \(\Rightarrow\left(x+2\right);\left(y-1\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét bảng 

x+2	1	-1	5	-5
y-1	5	-5	1	-1
x	1	-3	3	-7
y	6	-4	2	0

Vậy..............