Câu hỏi của Lê Sinh Hải

Question

5n + 2 chia hết cho 2n +9 >làm ơn nhanh giùm mình nha!

Nguyen Thi Huyen · Accepted Answer

Ta có: $\left(5n+2\right)⋮\left(2n+9\right)$ và $\left(2n+9\right)⋮\left(2n+9\right)$

$\Rightarrow\left\{{}\begin{matrix}2\left(5n+2\right)⋮\left(2n+9\right)\5\left(2n+9\right)⋮\left(2n+9\right)\end{matrix}\right.$ $\Rightarrow\left\{{}\begin{matrix}\left(10n+4\right)⋮\left(2n+9\right)\\left(10n+45\right)⋮\left(2n+9\right)\end{matrix}\right.$

$\Rightarrow\left(10n+45\right)-\left(10n+4\right)⋮\left(2n+9\right)$

$\Rightarrow41⋮\left(2n+9\right)$

$\Rightarrow\left(2n+9\right)\inƯ\left(41\right)$

$\Rightarrow\left(2n+9\right)\in\left\{\pm1;\pm41\right\}$

Ta có bảng sau:

$2n+9$
			$-41$
			$-1$
			$1$
			$41$

$2n$
			$-50$
			$-10$
			$-8$
			$32$

$n$
			$-25$
			$-5$
			$-4$
			$16$

Vậy $n\in\left\{-25;-5;-4;-16\right\}$ thì $\left(5n+2\right)⋮\left(2n+9\right).$Câu trả lời: Ta có: $\left(5n+2\right)⋮\left(2n+9\right)$ và $\left(2n+9\right)⋮\left(2n+9\right)$