Question

tìm n thuộc Z

a, n2 +3n -13 chia hết n + 3

Answer 1

\(n^2+3n-13⋮n+3\)

Mà \(n+3⋮n+3\)

\(\Leftrightarrow\left\{{}\begin{matrix}n^2+3n-13⋮n+3\\n^2+3n⋮n+3\end{matrix}\right.\)

\(\Leftrightarrow13⋮n+3\)

\(\Leftrightarrow n+3\inƯ\left(13\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+3=1\\n+3=13\\n+3=-1\\n+3=-13\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}n=-2\\n=10\\n=-4\\n=-16\end{matrix}\right.\)

Vậy ..

Answer 2

$n^2+3n-13⋮n+3$

Mà $n+3⋮n+3$

$\iff \{\begin{array}{c}{n}^2+3n-13⋮n+3\\ n^2+3n⋮n+3\end{array}$

$\iff 13⋮n+3$

$\iff n+3\in Ư\left(13\right)$

$\iff [\begin{array}{c}n+3=1\\ n+3=13\\ n+3=-1\\ n+3=-13\end{array}$

$\iff [\begin{array}{c}n=-2\\ n=10\\ n=-4\\ n=-16\end{array}$

Vậy ..