Ta có : \(\frac{3\sqrt{x}}{\sqrt{x}-3}=\left(\frac{3\sqrt{x}}{\sqrt{x}-3}\right)^4\)
- Đặt \(\frac{3\sqrt{x}}{\sqrt{x}-3}=a\) ta được :\(a^4=a\)
=> \(a^4-a=0\)
=> \(a\left(a^3-1\right)=0\)
=> \(\left[{}\begin{matrix}a=0\\a^3-1=0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}a=0\\a=1\end{matrix}\right.\)
- Thay lại x vào ta được :
\(\left[{}\begin{matrix}\frac{3\sqrt{x}}{\sqrt{x}-3}=0\\\frac{3\sqrt{x}}{\sqrt{x}-3}=1\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}3\sqrt{x}=0\\3\sqrt{x}=\sqrt{x}-3\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=0\\2\sqrt{x}=-3\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=0\left(TM\right)\\\sqrt{x}=-\frac{3}{2}\left(VL\right)\end{matrix}\right.\)
=> x = 0 .
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