Question

Tìm x ϵ Z để B nguyên

B=\(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)

Answer 1

ĐK: \(x\ge0;x\ne1\)

\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=1+\dfrac{2}{\sqrt{x}-1}\)

Để \(B\) nguyên \(\Leftrightarrow\left(\sqrt{x}-1\right)\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}-1=1\\\sqrt{x}-1=-1\\\sqrt{x}-1=2\\\sqrt{x}-1=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\sqrt{x}=2\\\sqrt{x}=0\\\sqrt{x}=3\\\sqrt{x}=-1\left(L\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=0\\x=9\end{matrix}\right.\left(TM\right)\)