Toán Lớp 6: Chứng minh rằng nếu abcd : 29 thì ( a + 3b + 9c + 27d ) :29

Question

Toán Lớp 6:  Chứng minh rằng nếu abcd : 29 thì ( a + 3b + 9c + 27d ) :29

diemchau · Answer

&macr;abcd⋮29     &hArr;2&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;abcd⋮29     &hArr;2(1000a+100b+10c+d)⋮29     &hArr;2000a+200b+20c+2d⋮29     &hArr;2001a&minus;a+203b&minus;3b+29c&minus;9c+29d&minus;27d⋮29     &hArr;(2001a+203b+29c+29d)&minus;(a+3b+9c+27d)⋮29     &hArr;29(69a+7b+c+d)&minus;(a+3b+9c+27d)⋮29     &hArr;a+3b+9c+27d⋮29

dinhcongson · Answer

Ta c&oacute; : abc  $ vdots$ 29&rArr; ( 1000a + 100b + 10c + d )   &rArr; 2000a + 200b + 20b + 2c $ vdots$ 29   &rArr; ( 2001a + 203b + 29c + 27d ) - ( a + 3b + 9c + 27 )  $ vdots$ 29   &rArr; 29 x ( 69a + 7b + c + d ) - ( a + 3b + 9c + 27 )  $ vdots$ 29   V&igrave; 29 x ( 69a + 7b + c + d ) $ vdots$ 29 v&agrave; 29 x ( 69a + 7b + c + d ) - ( a + 3b + 9c + 27 )  $ vdots$ 29   &rArr; a + 3b + 9c + 27 $ vdots$ 29