Question

Tìm x biết  (2x-5) chia hết cho (x-3)

HELP ME

Answer 1

Ta có : \(2x-5⋮x-3\)

\(\Rightarrow2x-6+1⋮x-3\)

\(\Rightarrow2\left(x-3\right)+1⋮x-3\)

Mà : \(2\left(x-3\right)⋮x-3\)suy ra : \(1⋮x-3\)

\(\Rightarrow x-3\inƯ\left(1\right)=\left\{-1;1\right\}\)

\(\Rightarrow x\in\left\{2;4\right\}\)

Answer 2

\(\left(2x-5\right)⋮\left(x-3\right)\)

\(\Rightarrow\left(2x-6+1\right)⋮\left(x-3\right)\)

Vì \(\left(2x-6\right)⋮\left(x-3\right)\)nên \(1⋮\left(x-3\right)\)

\(\Rightarrow x-3\inƯ\left(1\right)=\left\{\pm1\right\}\)

Trường hợp : \(x-3=-1\)

\(\Leftrightarrow x=-1+3\)

\(\Leftrightarrow x=2\)

Trường hợp : \(x-3=1\)

\(\Leftrightarrow x=1+4\)\(\Leftrightarrow x=5\)Vậy \(x\in\left\{2;5\right\}\)