Các số tự nhiên \(x\) sao cho:\(a,\ 8~\vdots \left...

C

- Hướng dẫn giải

Phương pháp giải:

\(U\left( a \right)=\left\{ x\in N|a\vdots x \right\}\).

Giải chi tiết:

 \(\begin{array}{l}a)\,8 \vdots \left( {x - 1} \right) \Rightarrow \left( {x - 1} \right) \in U\left( 8 \right)\\ \Rightarrow \left( {x - 1} \right) \in \left\{ {1;2;4;8} \right\}\\ \Rightarrow x \in \left\{ {2;3;5;9} \right\}\end{array}\)

\(\begin{array}{l}b)70 \vdots \left( {2x - 3} \right)\\70 \vdots \left( {2x - 3} \right) \Rightarrow \left( {2x - 3} \right) \in U\left( {70} \right)\\ \Rightarrow 2x - 3 \in \left\{ {1;2;5;7;10;14;35;70} \right\}\\ \Rightarrow 2x \in \left\{ {4;5;8;10;13;17;38;73} \right\}\\ \Rightarrow x \in \left\{ {2;4;5;19} \right\}\end{array}\)

\(\begin{array}{l}c)x + 2 \in U\left( {16} \right)\\ \Rightarrow x + 2 \in \left\{ {1;2;4;8;16} \right\}\\ \Rightarrow x \in \left\{ {0;2;6;14} \right\}\end{array}\)

\(\begin{array}{l}d)2x + 1 \in U\left( {21} \right)\\ \Rightarrow 2x + 1 \in \left\{ {1;3;7;21} \right\}\\ \Rightarrow 2x \in \left\{ {0;2;6;20} \right\}\\ \Rightarrow x \in \left\{ {0;1;3;10} \right\}\end{array}\)

Chọn C.