Bài 1:
\(a\left(b-2\right)=3\Rightarrow a\left(b-2\right)=Ư\left(3\right)\)
\(a\left(b-2\right)=a=Ư\left(3\right)=\left\{\pm1;\pm3\right\}\)
Mà \(a>0\Rightarrow a=\left\{1;3\right\}\)
\(\Rightarrow\left[\begin{matrix}a=1\Rightarrow b-2=3\Rightarrow b=5\\a=3\Rightarrow b-2=1\Rightarrow b=3\end{matrix}\right.\)
\(\Rightarrow a=\left\{1;3\right\},b=\left\{5;3\right\}\)
Bài 2:
\(S=-\left(a-b-c\right)+\left(-c+b+a\right)-\left(a+b\right)\)
\(=-a+b+c-c+b+a-a-b\)
\(=\left(-a+a-a\right)+\left(b+b-b\right)+\left(c-c\right)\)
\(=-a+b+0\)
\(=b-a\)
Vì \(a>b\Rightarrow\left|S\right|=a-b\)
Bài 3:
\(A+B=a+b-5+\left(-b-c+1\right)\)
\(=a+b-5-b-c+1=a-c-4\)(1)
\(C-D=b-c-4-\left(b-a\right)\)
\(=b-c-4-b+a=-c-4+a=a-c-4\)(2)
Từ (1) và (2) \(\Rightarrow A+B=C-D\)(Đpcm)
