có thể có ( nếu bn lm đúng ) ; có thể ko ( nếu bn lm sai )!
Đề: Tìm x nguyên sao cho (x+17)⋮(x-3)
\(\left(x+17\right)⋮\left(x-3\right)\)
\(\Rightarrow\left(x-3+20\right)⋮\left(x-3\right)\)
Vì \(\left(x+3\right)⋮\left(x+3\right)\)\(\Rightarrow20⋮x-3\)\(\Rightarrow x-3\inƯ\left(20\right)=\left\{\pm1;\pm2;\pm4;\pm5;\pm10;\pm20\right\}\)
\(\Rightarrow x\in\left\{-17;\pm7;\pm2;\pm1;4;5;8;13;23\right\}\)
\(\begin{cases} (x+17) ⋮ (x-3)\\ (x-3)⋮ (x-3) \end{cases} \)
⇒(x+17) - (x-3) ⋮ (x-3)
⇒20⋮ (x-3)
⇒x-3∈Ư(20)
⇒x∈{4;2;5;1;7;-1;8;-2;13;-7;23;-17}
Ta có: \(x+17⋮x-3\)
\(\Leftrightarrow x-3\in\left\{1;-1;2;-2;4;-4;5;-5;10;-10;20;-20\right\}\)
hay \(x\in\left\{4;2;5;1;7;-1;8;-2;13;-7;23;-17\right\}\)