Question

(2 căn x +1)(căn x -2)=7

Answer 1

\(ĐK:x\ge0\\ \left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\\ \Leftrightarrow2x-3\sqrt{x}-2=7\\ \Leftrightarrow2x-3\sqrt{x}-9=0\\ \Leftrightarrow\left(\sqrt{x}-3\right)\left(2\sqrt{x}+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\\2\sqrt{x}=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x\in\varnothing\end{matrix}\right.\Leftrightarrow x=9\left(tm\right)\)

Answer 2

\(\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\)

\(\Leftrightarrow2\sqrt{x}-3\sqrt{x}-9=0\)

\(\Leftrightarrow\sqrt{x}-3=0\)

hay x=9