Question

4n-15chia hết 2n-4

Answer 1

Ta có: \(4n-15⋮2n-4\)

\(\Leftrightarrow4n-8-7⋮2n-4\)

mà \(4n-8⋮2n-4\)

nên \(-7⋮2n-4\)

\(\Leftrightarrow2n-4\inƯ\left(-7\right)\)

\(\Leftrightarrow2n-4\in\left\{1;-1;7;-7\right\}\)

\(\Leftrightarrow2n\in\left\{5;3;11;-3\right\}\)

hay \(n\in\left\{\dfrac{5}{2};\dfrac{3}{2};\dfrac{11}{2}-\dfrac{3}{2}\right\}\)

Vậy: \(n\in\left\{\dfrac{5}{2};\dfrac{3}{2};\dfrac{11}{2}-\dfrac{3}{2}\right\}\)