\(8n+1⋮2n+1\)
\(\Rightarrow8n+1-4\left(2n+1\right)⋮2n+1\)
\(\Rightarrow8n+1-8n-4⋮2n+1\)
\(\Rightarrow-3⋮2n+1\)
\(\Rightarrow2n+1\in\left\{-1;1;-3;3\right\}\)
\(\Rightarrow n\in\left\{-1;0;-2;1\right\}\left(n\in N\right)\)
Xét phân số: \(A=\dfrac{8n+1}{2n+1}=\dfrac{8n+4-3}{2n+1}=\dfrac{8n+4}{2n+1}-\dfrac{3}{2n+1}=\dfrac{4\left(2n+1\right)}{2n+1}-\dfrac{3}{2n+1}=4-\dfrac{3}{2n+1}\)
8n + 1 chia hết cho 2n + 1 => A \(\in Z\) => 2n + 1 \(\inƯ\left(3\right)=\left\{-1,-3,1,3\right\}\)
Ta có bảng:
2n+1 | -1 | -3 | 1 | 3 |
n | -1 | -2 | 0 | 1 |
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