Toán voi x,y thuoc Z, 7x+3y chia het cho 13 ⇔ 5x+4y chia het cho 13 05/11/2021 By Ximena voi x,y thuoc Z, 7x+3y chia het cho 13 ⇔ 5x+4y chia het cho 13
$\,\,\,\,\,\,7x+3y\,\,\,\vdots \,\,\,13$ $\to 10\left( 7x+3y \right)\,\,\,\vdots \,\,\,\,13$ $\to 70x+30y\,\,\,\vdots \,\,\,13$ $\to 70x+30y-13.5x-13.2y\,\,\,\vdots \,\,\,13$ $\to 70x+30y-65x-26y\,\,\,\vdots \,\,\,13$ $\to 5x-4y\,\,\,\vdots \,\,\,13$ Trả lời
– Xét tổng : `3(7x+3y)+(5x+4y)` `=21x+9y+5x+4y` `=(21x+5x)+(9y+4y)` `=26x+13y` `=13(2x+y) vdots 13` `=> 3(7x+3y)+(5x+4y) vdots 13` mà `3(7x+3y) vdots 13` `=> 5x+4y vdots 13 text{(đpcm)}` Trả lời
$\,\,\,\,\,\,7x+3y\,\,\,\vdots \,\,\,13$
$\to 10\left( 7x+3y \right)\,\,\,\vdots \,\,\,\,13$
$\to 70x+30y\,\,\,\vdots \,\,\,13$
$\to 70x+30y-13.5x-13.2y\,\,\,\vdots \,\,\,13$
$\to 70x+30y-65x-26y\,\,\,\vdots \,\,\,13$
$\to 5x-4y\,\,\,\vdots \,\,\,13$
– Xét tổng :
`3(7x+3y)+(5x+4y)`
`=21x+9y+5x+4y`
`=(21x+5x)+(9y+4y)`
`=26x+13y`
`=13(2x+y) vdots 13`
`=> 3(7x+3y)+(5x+4y) vdots 13`
mà `3(7x+3y) vdots 13`
`=> 5x+4y vdots 13 text{(đpcm)}`