Question

Tìm các số tự nhiên a sao cho::

a)a+1 là ước của 5a+12                                                b)3a+20 chia hết cho a+2 

Answer 1

a) Vì \(a+1\inƯ\left(5a+12\right)\)nên:

\(\Rightarrow5a+12⋮a+1\)

\(\Rightarrow5.\left(a+1\right)+7⋮a+1\)

\(\Rightarrow7⋮a+1\)(vì \(5.\left(a+1\right)⋮a+1\))

\(\Rightarrow a+1\inƯ\left(7\right)\)

\(\Rightarrow a+1\in\left\{-7;-1;1;7\right\}\)

\(\Rightarrow a\in\left\{-8;-2;0;6\right\}\)

b) \(3a+20⋮a+2\)

\(\Rightarrow3.\left(a+2\right)+14⋮a+2\)

\(\Rightarrow a+2\inƯ\left(14\right)\)(vì \(3\left(a+2\right)⋮a+2\))

\(\Rightarrow a+2\in\left\{-1;-2;-7;-14;1;2;7;14\right\}\)

\(\Rightarrow a\in\left\{-3;-4;-9;-16;-1;0;5;12\right\}\)

Hok tốt nha^^