Câu hỏi của PHAN THÙY LINH

Question

Tim cac cap so nguyen x,y thoa man

a) xy-5x+y=17

b) x.(y-2)=3 va x>y

Kiệt Nguyễn · Accepted Answer

a) $xy-5x+y=17$

$\Leftrightarrow x\left(y-5\right)+y-5=12$

$\Leftrightarrow\left(x+1\right)\left(y-5\right)=12$

$\Leftrightarrow\left(x+1\right)\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}$

Ta có bảng sau :

$x+1$	$-12$	$-6$	$-4$	$-3$	$-2$	$-1$	$1$	$2$	$3$	$4$	$6$	$12$
$x$	$-13$	$-7$	$-5$	$-4$	$-3$	$-2$	$0$	$1$	$2$	$3$	$5$	$11$

Câu trả lời:

a) $xy-5x+y=17$

$\Leftrightarrow x\left(y-5\right)+y-5=12$

$\Leftrightarrow\left(x+1\right)\left(y-5\right)=12$

$\Leftrightarrow\left(x+1\right)\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}$

Ta có bảng sau :

$x+1$	$-12$	$-6$	$-4$	$-3$	$-2$	$-1$	$1$	$2$	$3$	$4$	$6$	$12$
$x$	$-13$	$-7$	$-5$	$-4$	$-3$	$-2$	$0$	$1$	$2$	$3$	$5$	$11$

Kiệt Nguyễn · Answer

b) $x\left(y-2\right)=3$

$\Leftrightarrow x\left(y-2\right)=3.1=-1.\left(-3\right)$

*Trường hợp 1: $x=3$

$\Leftrightarrow y-2=1$

$\Leftrightarrow y=1+2$

$\Leftrightarrow y=3$

*Trường hợp 1: $x=-1$

$\Leftrightarrow y-2=-3$

$\Leftrightarrow y=-3+2$

$\Leftrightarrow y=-2$

$\Rightarrow x=-1;y=-2$

Câu trả lời:

b) $x\left(y-2\right)=3$

$\Leftrightarrow x\left(y-2\right)=3.1=-1.\left(-3\right)$

*Trường hợp 1: $x=3$

$\Leftrightarrow y-2=1$

$\Leftrightarrow y=1+2$

$\Leftrightarrow y=3$

*Trường hợp 1: $x=-1$

$\Leftrightarrow y-2=-3$

$\Leftrightarrow y=-3+2$

$\Leftrightarrow y=-2$

$\Rightarrow x=-1;y=-2$

Đặng Tú Phương · Answer

$xy-5x+y=17$

$\Rightarrow x\left(y-5\right)+\left(y-5\right)=17-5$

$\Rightarrow\left(x+1\right)\left(y-5\right)=12$

$\Rightarrow\left(x+1\right)\left(y-5\right)\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}$

Ta có các trường hợp

$TH1:\hept{\begin{cases}x+1=1\y-5=12\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\y=17\end{cases}}}$

$TH2:\hept{\begin{cases}x+1=-1\y-5=-12\end{cases}\Leftrightarrow\hept{\begin{cases}x=-2\y=-7\end{cases}}}$

$TH3:\hept{\begin{cases}x+1=2\y-5=6\end{cases}\Leftrightarrow\hept{\begin{cases}x=1\y=11\end{cases}}}$

$TH4:\hept{\begin{cases}x+1=-2\y-5=-6\end{cases}\Leftrightarrow\hept{\begin{cases}x=-3\y=-1\end{cases}}}$

$TH5:\hept{\begin{cases}x+1=3\y-5=4\end{cases}\Leftrightarrow\hept{\begin{cases}x=2\y=9\end{cases}}}$

$TH6:\hept{\begin{cases}x+1=-3\y-5=-4\end{cases}\Leftrightarrow\hept{\begin{cases}x=-4\y=1\end{cases}}}$

$TH7:\hept{\begin{cases}x+1=12\y-5=1\end{cases}\Leftrightarrow\hept{\begin{cases}x=11\y=6\end{cases}}}$

$TH8:\hept{\begin{cases}x+1=-12\y-5=-1\end{cases}\Leftrightarrow\hept{\begin{cases}x=-13\y=4\end{cases}}}$

$TH9:\hept{\begin{cases}x+1=6\y-5=2\end{cases}\Leftrightarrow\hept{\begin{cases}x=5\y=7\end{cases}}}$

$TH10:\hept{\begin{cases}x+1=-6\y-5=-2\end{cases}\Leftrightarrow\hept{\begin{cases}x=-7\y=-3\end{cases}}}$

$TH11:\hept{\begin{cases}x+1=4\y-5=3\end{cases}\Leftrightarrow\hept{\begin{cases}x=3\y=8\end{cases}}}$

$TH12:\hept{\begin{cases}x+1=-4\y-5=-3\end{cases}\Leftrightarrow\hept{\begin{cases}x=-5\y=2\end{cases}}}$

Vậy.......................................

$x\left(y-2\right)=3$

$\Rightarrow x;\left(y-2\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}$

Ta có các trường hợp sau:

$TH1:\hept{\begin{cases}x=1\y-2=3\end{cases}\Leftrightarrow\hept{\begin{cases}x=1\y=5\end{cases}\left(loại\right)}}$

$TH2:\hept{\begin{cases}x=-1\y-2=-3\end{cases}\Leftrightarrow\hept{\begin{cases}x=-1\y-1\end{cases}\left(loại\right)}}$

$TH3:\hept{\begin{cases}x=3\y-2=1\end{cases}\Leftrightarrow\hept{\begin{cases}x=3\y=3\end{cases}}\left(loại\right)}$

$TH4:\hept{\begin{cases}x=-3\y-2=-3\end{cases}\Leftrightarrow\hept{\begin{cases}x=-3\y=-1\end{cases}\left(loại\right)}}$

Vậy.............................

p/s: câu b chưa chắc chắn nha