Toán Lớp 6: 1. tìm số nguyên n sao cho: 5n+2⋮2n-3
2. tìm số nguyên n sao cho: 4n+2⋮(2n-3)
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Toán Lớp 6: 1. tìm số nguyên n sao cho: 5n+2⋮2n-3
2. tìm số nguyên n sao cho: 4n+2⋮(2n-3)
Comments ( 1 )
Giải đáp:
\(\begin{array}{l}
1)\left[ \begin{array}{l}
n = 11\\
n = – 8\\
n = 2\\
n = 1
\end{array} \right.\\
2)\left[ \begin{array}{l}
n = 2\\
n = 1
\end{array} \right.
\end{array}\)
Lời giải và giải thích chi tiết:
\(\begin{array}{l}
1)5n + 2 \vdots 2n – 3\\
\to 10n + 4 \vdots 2n – 3\\
\to 5\left( {2n – 3} \right) + 19 \vdots 2n – 3\\
\to 19 \vdots 2n – 3\\
\to 2n – 3 \in U\left( {19} \right)\\
\to \left[ \begin{array}{l}
2n – 3 = 19\\
2n – 3 = – 19\\
2n – 3 = 1\\
2n – 3 = – 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 11\\
n = – 8\\
n = 2\\
n = 1
\end{array} \right.\\
2)4n + 2 \vdots 2n – 3\\
\to 2\left( {2n – 3} \right) + 8 \vdots 2n – 3\\
\to 8 \vdots 2n – 3\\
\to 2n – 3 \in U\left( 8 \right)\\
\to \left[ \begin{array}{l}
2n – 3 = 8\\
2n – 3 = – 8\\
2n – 3 = 4\\
2n – 3 = – 4\\
2n – 3 = 2\\
2n – 3 = – 2\\
2n – 3 = 1\\
2n – 3 = – 1
\end{array} \right. \to \left[ \begin{array}{l}
n = \dfrac{{11}}{2}\left( l \right)\\
n = – \dfrac{5}{2}\left( l \right)\\
n = \dfrac{7}{2}\left( l \right)\\
n = – \dfrac{1}{2}\left( l \right)\\
n = \dfrac{5}{2}\left( l \right)\\
n = \dfrac{1}{2}\left( l \right)\\
n = 2\\
n = 1
\end{array} \right.
\end{array}\)