x-2 là ước của 3x -13
\(\Rightarrow\)3x - 13 \(⋮\)x - 2
\(\Rightarrow\)( 3x - 6 ) - 7 \(⋮\)x - 2
\(\Rightarrow\)3.( x - 2 ) - 7 \(⋮\)x - 2
Vì x - 2 \(⋮\)x - 2
nên 3. ( x - 2) \(⋮\)x - 2
\(\Rightarrow\)7 \(⋮\)x - 2
\(\Rightarrow\)\(x-2\inƯ\left(7\right)\)
\(\Rightarrow\)\(x-2\in\left\{1;-1;7;-7\right\}\)
\(\Rightarrow\)\(x\in\left\{3;1;9;-5\right\}\)
Vậy \(x\in\left\{3;1;9;-5\right\}\)
~ HOK TỐT ~
nếu x - 2 là ước của 3 x - 13 thì 3x - 13 \(⋮\)x - 2
3x - 13 \(⋮\)x - 2\(\Leftrightarrow\)3x - 13 \(⋮\)x- 2
x - 2 \(⋮\)x - 2 \(\Leftrightarrow\)\(3(x-2)⋮x-2\)
\(\Rightarrow3x-13-3(x-2)⋮x-2\)
\(\Rightarrow-7⋮x-2\)\(\Rightarrow x-2\in\pm1,\pm7\)
\(x-2=-7\Rightarrow x=-5\)
\(x-2=7\Rightarrow x=9\)
\(x-2=-1\Rightarrow x=1\)
\(x-2=1\Rightarrow x=3\)
\(vậy\)\(x\in(-5,9,1,3)\)
