Question

Tìm x thuộc Z biết :

a) (x - 2 ) chia hết cho ( x+7 )

b) (2x + 1 ) chia hết cho( 2x - 3 )

Answer 1

a) \(x-2⋮x+7\)

\(x+7-9⋮x+7\)

Mà \(x+7⋮x+7\)

\(\Rightarrow-9⋮x+7\)

\(\Rightarrow x+7\inƯ\left(9\right)=\left\{\pm1;\pm3;\pm9\right\}\)

\(x+7\)	\(1\)	\(-1\)	\(3\)	\(-3\)	\(9\)	\(-9\)
\(x\)	\(-6\)	\(-8\)	\(-4\)	\(-10\)	\(2\)	\(-16\)

                    Vậy, \(x\in\left\{-16;-10;-8;-6;-4;2\right\}\)

b)  \(2x+1⋮2x-3\)

\(2x-3+4⋮2x-3\)

Mà \(2x-3⋮2x-3\)

\(\Rightarrow4⋮2x-3\)

\(\Rightarrow2x-3\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

     VÌ \(2x-3\)là số lẻ và \(x\inℤ\)

\(\Rightarrow2x-3\in\left\{\pm1\right\}\)

\(2x-3\)	\(1\)	\(-1\)
\(x\)	\(2\)	\(1\)

                    Vậy, \(x\in\left\{1;2\right\}\)