Question

Tìm x thuộc Z,biết:

a,-3 chia hết (x+1)

b,5 chia hết(x+2)

c,x+5 chia hết x+1

d,x -2 chia hết x+3

e,2x+3 chia hết x-1

Answer 1

a) \(-3⋮x+1\)

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

Ta có bảng sau:

\(x+1\)	\(-1\)	\(1\)	\(-3\)	\(3\)
\(x\)	\(-2\)	\(0\)	\(-4\)	\(2\)

KL: Vậy...

b) \(5⋮x+2\)

\(\Rightarrow x+2\inƯ\left(5\right)=\left\{-1;1;-5;5\right\}\)

Ta có bảng sau:

\(x+2\)	\(-1\)	\(1\)	\(-5\)	\(5\)
\(x\)	\(-3\)	\(-1\)	\(-7\)	\(3\)

KL: Vậy...

c) \(x+5⋮x+1\)

\(\Leftrightarrow x+1+4⋮x+1\)

Vì \(x+1⋮x+1\) nên \(4⋮x+1\Rightarrow x+1\inƯ\left(4\right)=\left\{-1;1;-4;4\right\}\)

Ta có bảng sau:

\(x+1\)	\(-1\)	\(1\)	\(-4\)	\(4\)
\(x\)	\(-2\)	\(0\)	\(-5\)	\(3\)

KL: Vậy...

d) \(x-2⋮x+3\)

\(\Leftrightarrow x+3-5⋮x+3\)

Vì \(x+3⋮x+3\) nên \(-5⋮x+3\Rightarrow x+3\inƯ\left(-5\right)=\left\{-1;1;-5;5\right\}\)

Ta có bảng sau:

\(x+3\)	\(-1\)	\(1\)	\(-5\)	\(5\)
\(x\)	\(-4\)	\(-2\)	\(-8\)	\(2\)

KL: Vậy...

e) \(2x+3⋮x-1\)

\(\Leftrightarrow2\left(x-1\right)+5⋮x-1\)

Vì \(2\left(x-1\right)⋮x-1\) nên \(5⋮x-1\Rightarrow x-1\inƯ\left(5\right)=\left\{-1;1;-5;5\right\}\)

Ta có bảng sau:

\(x-1\)	\(-1\)	\(1\)	\(-5\)	\(5\)
\(x\)	\(0\)	\(2\)	\(-4\)	\(6\)

KL: Vậy...