Cj gãy cổ rồi e ơi =))
a) Để biểu thức A có giá trị nguyên thì :
\(a+1⋮2a\)
Mà \(2a⋮2a\)
\(\Leftrightarrow\left\{{}\begin{matrix}2a+2⋮2a\\2a⋮2a\end{matrix}\right.\)
\(\Leftrightarrow2⋮2a\)
Vì \(a\in Z;2⋮2a\Leftrightarrow2a\inƯ\left(2\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2a=1\Leftrightarrow a=\dfrac{1}{2}\left(loại\right)\\2a=2\Leftrightarrow a=1\left(tm\right)\\2a=-1\Leftrightarrow a=\dfrac{-1}{2}\left(loại\right)\\2a=-2\Leftrightarrow a=-1\left(tm\right)\end{matrix}\right.\)
Vậy ..............
b) Để phân số \(\dfrac{a-2}{7}\in Z\) thì :
\(a-2⋮7\)
Vì \(a\in Z\Leftrightarrow a-7\in Z;a-7\inƯ\left(7\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}a-7=1\Leftrightarrow a=8\left(tm\right)\\a-7=7\Leftrightarrow a=14\left(tm\right)\\a-7=-1\Leftrightarrow a=6\left(tm\right)\\a-7=-7\Leftrightarrow0\left(tm\right)\end{matrix}\right.\)
Vậy .............
\(a+1⋮2a\)
\(\Rightarrow2a+2⋮2a\)
\(\Rightarrow2⋮2a\)
\(\Rightarrow1⋮a\Rightarrow a=\pm1\)
\(2a+1⋮a-3\)
\(\Rightarrow2a-6+7⋮a-3\)
\(\Rightarrow2\left(a-3\right)+7⋮a-3\)
Xét ước
\(a-2⋮7\)
\(\Rightarrow a-2\in B\left(7\right)\)
\(B\left(7\right)=\left\{0;7;14;....\right\}\)
\(a\in\left\{-2;5;12;....\right\}\)
Jup e nhé