10 tháng 8 2023 lúc 19:08
\(\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\) (ĐK: \(x\ge0\))
\(\Leftrightarrow2x-4\sqrt{x}+\sqrt{x}-2=7\)
\(\Leftrightarrow2x-3\sqrt{x}-2-7=0\)
\(\Leftrightarrow2x-3\sqrt{x}-9=0\)
\(\Leftrightarrow2x+3\sqrt{x}-6\sqrt{x}-9=0\)
\(\Leftrightarrow\sqrt{x}\left(2\sqrt{x}+3\right)-3\left(2\sqrt{x}+3\right)=0\)
\(\Leftrightarrow\left(2\sqrt{x}+3\right)\left(\sqrt{x}-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=-\dfrac{3}{2}\text{(vô lý)}\\\sqrt{x}=3\end{matrix}\right.\)
\(\Leftrightarrow x=9\left(tm\right)\)
Vậy x=9
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