Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.\overline {12x3} \vdots 3 \Leftrightarrow \left\{ \begin{array}{l}
(1 + 2 + x + 3) \vdots 3\\
x \in N
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {6 + x} \right) \vdots 3\\
x \in N
\end{array} \right. \to x \in \left\{ {0;3;6;9} \right\}\\
b.\left\{ \begin{array}{l}
\overline {4x} \vdots 3\\
\overline {4x} \vdots 5
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left( {4 + x} \right) \vdots 3\\
\left[ \begin{array}{l}
x = 0 \to 4 \vdots 3\left( l \right)\\
x = 5 \to \left( {4 + 5} \right) \vdots 3
\end{array} \right.
\end{array} \right.\\
\to x = 5\\
c.\left\{ \begin{array}{l}
\overline {x12y} \vdots 2\\
\overline {x12y} \vdots 3\\
\overline {x12y} \vdots 5
\end{array} \right. \to \left\{ \begin{array}{l}
y = 0\\
\left( {x + 1 + 2 + 0} \right) \vdots 3\\
x \in N*
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 0\\
\left( {3 + x} \right) \vdots 3\\
x \in N*
\end{array} \right. \to \left\{ \begin{array}{l}
y = 0\\
x \in \left\{ {3;6;9} \right\}
\end{array} \right.
\end{array}\)
d. \(\overline {x04y} \) chia 5 dư 3
\( \Leftrightarrow y \in \left\{ {3;8} \right\}\)
mà
\(\begin{array}{l}
\left\{ \begin{array}{l}
\overline {x04y} \vdots 2\\
\overline {x04y} \vdots 3
\end{array} \right. \to \left\{ \begin{array}{l}
y = 8\\
\left( {x + 0 + 4 + 8} \right) \vdots 3\\
x \in N*
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 8\\
x \in \left\{ {3;6;9} \right\}
\end{array} \right.
\end{array}\)
