Question

tìm số nguyên a để số hữu tỉ x = -2023/a+7

Answer 1

Ta có: \(x=-\dfrac{2023}{a+7}\left(a\ne-7;x\ne0\right)\)

\(\Rightarrow\left(a+7\right)x=-2023\)

\(\Leftrightarrow ax=-7x-2023\)

\(\Leftrightarrow a=-\dfrac{7x+2023}{x}=-7-\dfrac{2023}{x}\)

Do \(a\in Z\Rightarrow\dfrac{2023}{x}\in Z\Rightarrow x\inƯ\left(2023\right)=\left\{\pm1;\pm7;\pm17\pm119;\pm289;\pm2023\right\}\)