Toán Lớp 6: Cho: B=2.n+9 Tìm n để: B chia hết cho n B chia hết cho [n+1]

Question

Toán Lớp 6:  Cho: B=2.n+9          Tìm n để: B chia hết cho n                            B chia hết cho [n+1]

myngocla · Answer

để  B chia hết cho n th&igrave; 2.n+9 $ vdots$ n     => 2n +9 $ vdots$ n     m&agrave; 2n $ vdots$ n      => 9 $ vdots$ n     => n &isin; Ư(9)     m&agrave; Ư(9)={&plusmn;1;&plusmn;3;&plusmn;9}     =>n &isin;{&plusmn;1;&plusmn;3;&plusmn;9}     để B chia hết cho n+1 th&igrave; 2.n+9 $ vdots$ n+1     => 2n+9  $ vdots$ n+1     =>2n+2+7  $ vdots$ n+1     =>2.(n+1)+7  $ vdots$ n+1     m&agrave; 2.(n+1)  $ vdots$ n+1     => 7  $ vdots$ n+1     =>   n+1   &isin;Ư(7)     m&agrave; Ư(7)={-7;-1;1;7}     =>  n+1   &isin;{-7;-1;1;7}     =>n &isin;{-8;-2;0;6}

hatuanlan · Answer

Muốn B vdots n th&igrave; 2.n+9 ⋮ n  => 2n +9 ⋮ n  M&agrave; 2n ⋮ n   => 9 ⋮ n  => n &isin; Ư(9)  M&agrave; Ư(9)={&plusmn;1;&plusmn;3;&plusmn;9}  =>n &isin;{&plusmn;1;&plusmn;3;&plusmn;9}   Muốn B vdots n+1 th&igrave; 2.n+9 ⋮ n+1  => 2n+9  ⋮ n+1  =>2n+2+7  ⋮ n+1  =>2.(n+1)+7  ⋮ n+1  M&agrave; 2.(n+1)  ⋮ n+1  => 7  ⋮ n+1  =>   n+1   &isin;Ư(7)  M&agrave; Ư(7)={-7;-1;1;7}  =>  n+1   &isin;{-7;-1;1;7}  =>n &isin;{-8;-2;0;6}