Question

P = \(\dfrac{4x}{\sqrt{x}-3}\)

Tìm x biết \(\left|P\right|=-P\)

Answer 1

ĐK: \(x\ge0;x\ne9\)

\(\left|P\right|=-P\)

\(\Leftrightarrow P\le0\)

\(\Leftrightarrow\dfrac{4x}{\sqrt{x}-3}\le0\)

\(\Leftrightarrow\left\{{}\begin{matrix}4x\ge0\\\sqrt{x}-3< 0\end{matrix}\right.\left(I\right)\) hoặc \(\left\{{}\begin{matrix}4x\le0\\\sqrt{x}-3>0\end{matrix}\right.\left(II\right)\)

\(\left(I\right)\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}< 3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x< 9\end{matrix}\right.\Leftrightarrow0\le x< 9\)

\(\left(II\right)\Leftrightarrow\left\{{}\begin{matrix}x\le0\\\sqrt{x}>3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le0\\x>9\end{matrix}\right.\Rightarrow\) vô nghiệm

Vậy \(0\le x< 9\)