Question

tìm số nguyên x dể 2x² - x +2 chia hết cho 2x+1

Answer 1

Ta có :

\(2x^2-x+2\)

\(=2x^2+x-2x+2\)

\(=\left(2x^2+x\right)+2-2x\)

\(=x\left(2x+1\right)+2-2x\)  \(\text{⋮}\)\(2x+1\)

Mà \(x\left(2x+1\right)\)\(\text{⋮}\)\(2x+1\)

\(\Rightarrow2-2x\)\(\text{⋮}\)\(2x+1\)

Mà \(2x+1\)\(\text{⋮}\)\(2x+1\)

\(\Rightarrow\left(2-2x\right)+\left(2x+1\right)\)\(\text{⋮}\)\(2x+1\)

\(\Rightarrow3\)\(\text{⋮}\)\(2x+1\)

\(\Rightarrow2x+1\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(2x\in\left\{-4;-2;0;2\right\}\)

\(x\in\left\{-2;-1;0;1\right\}\)

Vậy ...