Question

Tìm các cặp số nguyên sao cho −7x −11 chia hết cho 2x + 4 .

Answer 1

\(\left(-7x-11\right)⋮\left(2x+4\right)\)

\(\Rightarrow2\left(-7x-11\right)⋮\left(2x+4\right)\)

\(\Rightarrow\left(-7x-11\right)⋮\left(x+2\right)\)

\(\Rightarrow\left(-7x-14+3\right)⋮\left(x+2\right)\)

\(\Rightarrow-7\left(x+2\right)+3⋮\left(x+2\right)\)

\(\Rightarrow3⋮\left(x+2\right)\)

\(\Rightarrow x+2=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(\Rightarrow x=\left\{-5;-3;-1;1\right\}\)

Thử lại thấy đều thỏa mãn, vậy \(x=\left\{-5;-3;-1;1\right\}\)