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: $x=-1$

$\Leftrightarrow y-2=-3$

$\Leftrightarrow y=-3+2$

$\Leftrightarrow y=-2$

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