Question

Tìm x,y nguyên thỏa mãn : xy+x+y+1=2

ai trả lời thì mình sẽ tick cho

Answer 1

Ta có : xy + x + y + 1 = 2

<=> xy + x + y + 1 = 2

<=> x(y + 1) + y + 1 = 2

<=> x(y + 1) + (y + 1) = 2

<=> (y + 1).(x + 1) = 2

Do đó y + 1 ; x + 1 thuộc Ư(2) = {-2;-1;1;2}

Ta có bảng : 

y + 1	-2	-1	1	2
x + 1	-1	-2	2	1
y	-3	-2	0	1
x	-2	-3	1	0

Answer 2

\(xy+x+y+1=2\)

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

\(\Rightarrow\left(x+1\right)y+x-2+1=0\)

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

\(\Rightarrow x+1\ne0;y=\frac{1-x}{x+1}\)

Answer 3

\(x=-3;-2;0;1\)

\(y=-2;-3;1;0\)