\(\Leftrightarrow2x-4\sqrt{x}-\sqrt{x}+2=7\)
\(\Leftrightarrow2x-5\sqrt{x}-5=0\)
\(\Leftrightarrow x-\dfrac{5}{2}\sqrt{x}-\dfrac{5}{2}=0\)
\(\Leftrightarrow x-2\cdot\sqrt{x}\cdot\dfrac{5}{4}+\dfrac{25}{16}=\dfrac{65}{16}\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-\dfrac{5}{4}=\dfrac{\sqrt{65}}{4}\\\sqrt{x}-\dfrac{5}{4}=-\dfrac{\sqrt{65}}{4}\end{matrix}\right.\Leftrightarrow x=\dfrac{45+5\sqrt{65}}{8}\)
ĐKXĐ: \(x\ge0\)
Đặt \(\sqrt{x}=t\ge0\)
\(\Rightarrow\left(2t-1\right)\left(t-2\right)=7\)
\(\Leftrightarrow2t^2-5t+2=7\)
\(\Leftrightarrow2t^2-5t-5=0\)
\(\Rightarrow\left[{}\begin{matrix}t=\dfrac{5+\sqrt{65}}{4}\\t=\dfrac{5-\sqrt{65}}{4}< 0\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x}=\dfrac{5+\sqrt{65}}{4}\)
\(\Rightarrow x=\left(\dfrac{5+\sqrt{65}}{4}\right)^2=\dfrac{45+5\sqrt{65}}{8}\)
\(ĐK:x\ge0\\ PT\Leftrightarrow2x-5\sqrt{x}+2=7\\ \Leftrightarrow2x-5\sqrt{x}-5=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=\dfrac{5+\sqrt{65}}{4}\\\sqrt{x}=\dfrac{5-\sqrt{65}}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{45+5\sqrt{65}}{8}\\x=\dfrac{45-5\sqrt{65}}{8}\end{matrix}\right.\)
