Question

P= √x-2/√+1 Tìm tất cả các giá trị nguyên của x để 2√P < 1

Answer 1

Sửa đề: \(P=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)

ĐKXĐ: x>=0

\(2\sqrt{P}< 1\)

=>\(\sqrt{P}< \dfrac{1}{2}\)

=>\(0< =P< \dfrac{1}{4}\)

=>\(\left\{{}\begin{matrix}P>=0\\P-\dfrac{1}{4}< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{\sqrt{x}-2}{\sqrt{x}+1}>=0\\\dfrac{\sqrt{x}-2}{\sqrt{x}+1}-\dfrac{1}{4}< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\sqrt{x}-2>=0\\\dfrac{4\left(\sqrt{x}-2\right)-\sqrt{x}-1}{4\left(\sqrt{x}+1\right)}< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\sqrt{x}>=2\\4\sqrt{x}-8-\sqrt{x}-1< 0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\sqrt{x}>=2\\3\sqrt{x}< 7\end{matrix}\right.\Leftrightarrow2< =\sqrt{x}< \dfrac{7}{3}\)

=>\(4< =x< \dfrac{49}{9}\)