Question

Tìm các số tự nhiên x sao cho : 

1/ ( x + 2 ) ⋮ ( x + 1 ) 

2/ ( x + 5 ) ⋮ ( x + 1 ) 

3/ ( x + 4 ) ⋮ ( x + 3 )

4/ ( x + 3 ) ⋮ ( x + 2 )

Giúp mk nhé ! Mk cần gấp lắm !

Answer 1

2, 

Ta có : \(\left(x+5\right)⋮\left(x+1\right)\)

\(\Leftrightarrow\frac{x+5}{x+1}\in N\Leftrightarrow\frac{x+1+4}{x+1}=\frac{x+1}{x+1}+\frac{4}{x+1}=1+\frac{4}{x+1}\)

Vì \(1\in N\)

\(\Leftrightarrow\frac{4}{x+1}\in N\Leftrightarrow x+1\inƯ_4=\left\{1;2;4\right\}\)

\(\Rightarrow x=\left\{0;1;3\right\}\)

mỏi tay quá ~ bạn làm nốt 2 ý còn lại nha .

Answer 2

1,

Ta có : \(\left(x+2\right)⋮\left(x+1\right)\)

\(\Leftrightarrow\frac{x+2}{x+1}\in N\Leftrightarrow\frac{x+1+1}{x+1}=\frac{x+1}{x+1}+\frac{1}{x+1}=1+\frac{1}{x+1}\)

Vì \(1\in N\)

\(\Rightarrow\frac{1}{n+1}\in N\Leftrightarrow n+1\inƯ_1=\left\{1\right\}\).

\(\Rightarrow n=\left\{0\right\}\)