$\text{a, 2x+3 $\vdots$ x}$
$\text{⇔ 3 $\vdots$ x}$
$\text{Hay x $\in$ Ư(3)={±1;±3}}$
$\text{Vậy x $\in$ {±1;±3}}$
$\text{b, 8x + 4 $\vdots$ 2x - 1}$
$\text{⇔8x - 4 + 8 $\vdots$ 2x - 1}$
$\text{⇔ 8 $\vdots$ 2x - 1}$
$\text{Hay 2x-1 $\in$ Ư(8)={±1;±2;±4;±8}}$
$\text{Ta có bảng sau :}$
\begin{array}{|c|c|c|}\hline \text{2x-1}&\text{-8}&\text{-4}&\text{-2}&\text{-1}&\text{1}&\text{2}&\text{4}&\text{8}\\\hline \text{x}&\text{$\frac{-7}{2}$ }&\text{$\frac{-3}{2}$ }&\text{$\frac{-1}{2}$ }&\text{0}&\text{1}&\text{$\frac{3}{2}$ }&\text{$\frac{5}{2}$ }&\text{$\frac{9}{2}$ }\\\hline \text{Kết quả}&\text{(L)}&\text{(L)}&\text{(L)}&\text{(TM)}&\text{(TM)}&\text{(L)}&\text{(L)}&\text{(L)}\\\hline\end{array}
$\text{ Vậy x $\in$ {0;1}}$
$\text{c, $x^{2}$ - x + 5x + 1 $\vdots$ x-1}$
$\text{⇔$x^{2}$ -2x +6x + 1 $\vdots$ x-1}$
$\text{⇔$(x-1)^{2}$+6x $\vdots$ x-1}$
$\text{⇔ 6x -6 +6 $\vdots$ x-1}$
$\text{⇔ 6 $\vdots$ x-1}$
$\text{Hay x-1 $\in$ Ư(6)={±1;±2;±3;±6}}$
$\text{Ta có bảng sau :}$
\begin{array}{|c|c|c|}\hline \text{x-1}&\text{-6}&\text{-3}&\text{-2}&\text{-1}&\text{1}&\text{2}&\text{3}&\text{6}\\\hline \text{x}&\text{-5}&\text{-2}&\text{-1}&\text{0}&\text{2}&\text{3}&\text{4}&\text{7}\\\hline \text{Kết quả}&\text{(TM)}&\text{(TM)}&\text{(TM)}&\text{(TM)}&\text{(TM)}&\text{(TM)}&\text{(TM)}&\text{(TM)}\\\hline\end{array}
$\text{ Vậy x $\in$ {-5;-2;-1;0;2;3;4;7}}$
CHO MK CTLHN NHA:(
