Question

Tìm x biết \(x\in Z\)

\(3x+2⋮x+1\)

\(x^2+2x-7⋮x+2\)

Answer 1

Ta có: 3x + 2 chia hết cho n + 1

<=> 3x + 3 - 1 chia hết cho n + 1

<=> 3.(n + 1) - 1 chia hết cho n + 1

<=> 1 chia hết cho n + 1

=> n + 1 thuộc Ư(1) = {-1;1}

Ta có bảng :

n + 1	-1	1
n	-2	0

Answer 2

\(3x+2⋮x+1\Rightarrow3x+3-1⋮x+1\)

\(\Rightarrow1⋮x+1\Rightarrow x+1\inƯ\left(1\right)\)

\(\Rightarrow\orbr{\begin{cases}x+1=-1\\x+1=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1-1=-2\\x=1-1=0\end{cases}}\)

Answer 3

\(x^2+2x-7⋮x+2\)

\(\Rightarrow x.x+2x-7⋮x+2\)

\(\Rightarrow x.x+2x+4-11⋮x+2\)

\(\Rightarrow x.x-11⋮x+2\)

\(\Rightarrow x.x-11⋮x.1-11+13\)