Question

a) 5n-1 chia hết cho 2n-7
b) 7n+3 chia hết cho 2n+5

Answer 1

\(a,5n-1⋮3n-7\)

\(15n-3⋮3n-7\)

\(5\left(3n-7\right)+32⋮3n-7\)

\(\Rightarrow32⋮3n-7\)

\(\Rightarrow3n-7\)là ước của \(32\)

\(\Rightarrow3n-7\in\left\{-32;-16;-8;-4;-2;-1;1;2;4;8;16;32\right\}\)

\(\Rightarrow3n\in\left\{-25;-9;-1;3;5;6;8;9;11;15;23;39\right\}\)

\(\Rightarrow n\in\left\{-3;1;2;3;5;13\right\}\left(n\in Z\right)\)

\(b,7n+3⋮2n+5\)

   \(14n+6⋮2n+5\)

   \(7\left(2n+5\right)-29⋮2n+5\)

    \(\Rightarrow29⋮2n+5\)

    \(\Rightarrow2n+5\in\left\{-29;-1;1;29\right\}\)

    \(\Rightarrow2n\in\left\{-34;-6;-4;24\right\}\)

    \(\Rightarrow n\in\left\{-17;-3;-2;12\right\}\)