a, Ta có : \(\left(x-5\right)⋮\left(x+1\right)\)
\(\Rightarrow\left(x+1-6\right)⋮\left(x+1\right)\)
\(\Rightarrow6⋮\left(x+1\right)\)
\(\Rightarrow x+1\inƯ\left(6\right)\)
Mà \(Ư\left(6\right)=\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
\(\Rightarrow x+1\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
\(\Rightarrow x\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)
b, gọi 2 số nguyên cần tìm là a,b
Ta có : \(a+b=a.b\)
\(\Rightarrow ab+a-b=0\)
\(\Rightarrow a\left(b+1\right)-b=0\)
\(\Rightarrow a\left(b+1\right)-b-1=-1\)
\(\Rightarrow a\left(b+1\right)-\left(b+1\right)=-1\)
\(\Rightarrow\left(b+1\right)\left(a-1\right)=-1\)
\(\Rightarrow b+1;a-1\) là ước của -1
Với \(b+1=-1\Rightarrow b=-2\)
\(a-1=1\Rightarrow a=2\)
Với \(b+1=1\Rightarrow b=0\)
\(a-1=-1\Rightarrow a=0\)
Vậy b = - 2 b = 0
a = 2 a = 0
