Question

Giúp mk nha!

Tìm số nguyên n biết \(2n+1⋮\left(n-3\right)\)

Answer 1

\(\frac{2n+1}{n-3}=\frac{2\left(n-3\right)+7}{n-3}=\frac{2\left(n-3\right)}{n-3}+\frac{7}{n-3}=2+\frac{7}{n-3}\in Z\)

Suy ra \(7⋮n-3\Rightarrow n-3\inƯ\left(7\right)=\left\{1;-1;7;-7\right\}\)

\(\Rightarrow n\in\left\{4;2;10;-4\right\}\left(n\in Z\right)\)

Answer 2

2n + 1 \(⋮\) n - 3

\(\Leftrightarrow\) 2n - 6 + 7 \(⋮\) n - 3

\(\Leftrightarrow\) 2(n - 3) + 7 \(⋮\) n- 3

\(\Leftrightarrow\) 7 \(⋮\) n - 3

\(\Leftrightarrow\) n - 3 \(\in\) {-7; -1; 1; 7}

\(\Leftrightarrow\) n \(\in\) {-4; 2; 4; 10} (n \(\in\) Z)

Answer 3

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