tìm các số nguyên n sao cho a , 3n + 2 : n – 1 b , 3n + 24 : n – 4 c, n^2 + 5 : n + 1 11/10/2021 Bởi Maya tìm các số nguyên n sao cho a , 3n + 2 : n – 1 b , 3n + 24 : n – 4 c, n^2 + 5 : n + 1
`a)“ 3n+2 \vdots n-1` `⇔5 \vdots n-1` `⇔n-1∈{±5;±1}` `⇔n∈{6;-4;2;0}` `b) 3n+24 \vdots n-4` `⇔36 \vdots n-4` `⇔n-4∈{±36;±1;±2;±3;±4;±6;±12;±9;±18}` `⇔n∈{40;-32;6;2;5;3;7;0;10;-2;16;-8;13;4;22;14}` `c)n^2+5 \vdots n+1` `⇔(n+1)^2 -2n-2+2+4 \vdots n+1` `⇔6 \vdots n+1` `⇔n+1∈{±1;±2;±3;±6}` `⇔n∈{0;1;2;5;-2;-3;-4;-7}` $@FBoy24$ Bình luận
`a)(3n+2)`$\vdots$`n-1` `⇒[3(n-1)+5]`$\vdots$`n-1` `⇒5`$\vdots$`n-1` `⇒n-1∈Ư(5)={±1,±5}` `⇒n∈{2,0,6,-4}` `b)(3n+24)`$\vdots$`n-4` `⇒[3(n-4)+36]`$\vdots$`n-4` `⇒36`$\vdots$`n-4` `⇒n-4∈Ư(36)={±1,±2,±3,±4,±6,±9,±12,±18,±36}` `⇒n∈{5,3,6,2,7,1,8,0,10,-2,13,-5,16,-8,22,-14,40,-32}` `c)(n^2+5)`$\vdots$`n+1` `⇒ [(n^2-1)+6]` $\vdots$`n+1` `⇒[(n-1)(n+1)+6]` $\vdots$`n+1` `⇒6` $\vdots$`n+1` `⇒n+1∈Ư(6)={±1,±2,±3,±6}` `⇒n∈{0,-2,1,-3,2,-4,5,-7}` Bình luận
`a)“ 3n+2 \vdots n-1`
`⇔5 \vdots n-1`
`⇔n-1∈{±5;±1}`
`⇔n∈{6;-4;2;0}`
`b) 3n+24 \vdots n-4`
`⇔36 \vdots n-4`
`⇔n-4∈{±36;±1;±2;±3;±4;±6;±12;±9;±18}`
`⇔n∈{40;-32;6;2;5;3;7;0;10;-2;16;-8;13;4;22;14}`
`c)n^2+5 \vdots n+1`
`⇔(n+1)^2 -2n-2+2+4 \vdots n+1`
`⇔6 \vdots n+1`
`⇔n+1∈{±1;±2;±3;±6}`
`⇔n∈{0;1;2;5;-2;-3;-4;-7}`
$@FBoy24$
`a)(3n+2)`$\vdots$`n-1`
`⇒[3(n-1)+5]`$\vdots$`n-1`
`⇒5`$\vdots$`n-1`
`⇒n-1∈Ư(5)={±1,±5}`
`⇒n∈{2,0,6,-4}`
`b)(3n+24)`$\vdots$`n-4`
`⇒[3(n-4)+36]`$\vdots$`n-4`
`⇒36`$\vdots$`n-4`
`⇒n-4∈Ư(36)={±1,±2,±3,±4,±6,±9,±12,±18,±36}`
`⇒n∈{5,3,6,2,7,1,8,0,10,-2,13,-5,16,-8,22,-14,40,-32}`
`c)(n^2+5)`$\vdots$`n+1`
`⇒ [(n^2-1)+6]` $\vdots$`n+1`
`⇒[(n-1)(n+1)+6]` $\vdots$`n+1`
`⇒6` $\vdots$`n+1`
`⇒n+1∈Ư(6)={±1,±2,±3,±6}`
`⇒n∈{0,-2,1,-3,2,-4,5,-7}`