Toán Lớp 6: tìm n thuộc Z sao cho : a,n+7 chia hết cho n+2 ; b,2n+3 chia hết cho 2n-2 c, 2n+1 chia hết cho 2-3n

Question

Toán Lớp 6:  tìm n thuộc Z sao cho : a,n+7 chia hết cho n+2 ;  b,2n+3 chia hết cho 2n-2  c, 2n+1 chia hết cho 2-3n

cobebongdem · Answer

a)n+7  vdots n+2   =>(n+7)-(n+2)  vdots n+2   =>[(n-n)+(7-2)]  vdots n+2   =>[0+5]  vdots n+2   =>5  vdots n+2   =>n+2&isin;(Ư)5={-1;1;-5;5}   =>n&isin;{(-1)-2;1-2;(-5)-2;5-2}   =>n&isin;{-3;-1;-7;3}   b)2n+3  vdots 2n-2   =>[(2n+3)-(2n-2)]  vdots 2n-2   =>[(2n-2n)+(3+2)]  vdots 2n-2   =>[0+5]  vdots 2n-2   =>5  vdots 2n-2   =>2n-2&isin;(Ư)5={-1;1;-5;5}   =>2n&isin;{1;3;-3;7}   =>n  ne 0   c)2n+1  vdots 2-3n   =>6(2n+1)  vdots 2-3n   =>6n+1  vdots 2-3n   =>6n-3n+1  vdots 2-3n   =>3(2-3n )+2  vdots 2n-3   =>2  vdots 2n-3   =>2n-3&isin;(Ư)2={1;2;-1;-2}   => n  ne 0

dongoctuan · Answer

a)n+7 chia hết cho n+2           $=>(n+7)-(n+2)&divide;(n+2)$         $=>5&divide;(n+2)$         $=>(n+2)&isin;Ư(5)={-1; -5; 1; 5}$         $=>n={-3; -7; -1; 3}$          b,2n+3 chia hết cho 2n-2           $=>(2n+3)-(2n-2)&divide;(2n-2)$           $=>5&divide;(2n-2)$           $=>(2n-2)&isin;Ư(5)={-1; -5; 1; 5}$                 $=>2n={1; -3; 3; 7}$           $=>n&isin;{&empty; }$           c, 2n+1 chia hết cho 2-3n           $=>3(2n+1)-2(2-3n)&divide;(2-3n)$           $=>(6n+3)-(4-6n)&divide;(2-3n)$           $=>6n+3-4+6n&divide;(2-3n)$           $=>6n-1+6n&divide;(2-3n)$           $=>12n-1&divide;(2-3n)$