Question

a)Tìm các số nguyên x,y biết xy - x - y = 2

b)Tìm số nguyên n để phân số sau là phân số nguyên A=\(\dfrac{3n-9}{n-2}\) B=\(\dfrac{4n+1}{n-1}\)

Answer 1

\(xy-x-y=2\)

\(\Rightarrow xy-x-y+1=3\)

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

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

\(\Rightarrow x-1;y-1\inƯ\left(3\right)\)

\(Ư\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=1\Rightarrow x=2\\y-1=3\Rightarrow y=4\\x-1=-1\Rightarrow x=0\\y-1=-3\Rightarrow y=-2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=3\Rightarrow x=4\\y-1=1\Rightarrow y=2\\x-1=-3\Rightarrow x=-2\\y-1=-1\Rightarrow y=0\end{matrix}\right.\)

b dễ,tự làm

Answer 2

xy-x-y=2

x(y-1)-(y-1)=1

(y-1).(x-1)=1

=>x-1 và y-1 \(\inƯ\left(1\right)=\left\{-1;1\right\}\)

x-1	-1	1
y-1	-1	1
x	0	2
y	0	2

Vậy (x,y)={(0,0);(2,2)}

Answer 3

Để A nguyên thì :

\(3n-9⋮n-2\)

\(3\left(n-2\right)-3⋮n-2\)

\(\Rightarrow3⋮n-2\Rightarrow n-2\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)

n-2	-3	-1	1	3
n	-1	1	3	5

Phần B TƯƠNG TỰ