Bài 1:ĐKXĐ: \(a\ne1\)
Để P nguyên thì \(2a⋮a-1\)
=>\(2a-2+2⋮a-1\)
=>\(2⋮a-1\)
=>\(a-1\in\left\{1;-1;2;-2\right\}\)
=>\(a\in\left\{2;0;3;-1\right\}\)
Bài 2:
ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne1\end{matrix}\right.\)
Để A nguyên thì \(\sqrt{x}+1⋮\sqrt{x}-1\)
=>\(\sqrt{x}-1+2⋮\sqrt{x}-1\)
=>\(2⋮\sqrt{x}-1\)
=>\(\sqrt{x}-1\in\left\{1;-1;2;-2\right\}\)
=>\(\sqrt{x}\in\left\{2;0;3\right\}\)
=>\(x\in\left\{0;4;9\right\}\)
Bài 3:
a: \(\left\{{}\begin{matrix}x-2y=4\\-3x+6y=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-6y=12\\-3x+6y=-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-6y-3x+6y=12-12\\x-2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0y=0\\x=2y+4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y\in R\\x=2y+4\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}-2x+y=5\\x+3y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x+y=5\\2x+6y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x+y+2x+6y=5+2\\x+3y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7y=7\\x=1-3y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=1-3=-2\end{matrix}\right.\)
Bài 4:
ĐKXĐ: x>=0
Để B nguyên thì \(2\sqrt{x}+7⋮\sqrt{x}+1\)
=>\(2\sqrt{x}+2+5⋮\sqrt{x}+1\)
=>\(5⋮\sqrt{x}+1\)
=>\(\sqrt{x}+1\in\left\{1;5\right\}\)
=>\(x\in\left\{0;16\right\}\)
