\(x-\sqrt{4x-3}=2\)
đặt \(T=\sqrt{4x-3}\)
\(\Leftrightarrow\left(x-T\right)^2-4=0\Leftrightarrow\left(x-T-2\right)\left(x-T+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=T+2\\x=T-2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{4x-3}+2\\x=\sqrt{4x-3}-2\end{matrix}\right.\)
Vậy nghiệm của pt là \(\left[{}\begin{matrix}x=\sqrt{4x-3}+2\\x=\sqrt{4x-3}-2\end{matrix}\right.\)
Đặt t=\(\sqrt{4x-3}\left(ĐK:t\ge0\right)\) và \(t^2=4x-3\)(!))
(!) \(\Leftrightarrow x=\dfrac{t^2+3}{4}\)
Pt \(\Leftrightarrow\dfrac{t^2+3}{4}-t=2\)
\(\Leftrightarrow t^2+3-4t=8\)
\(\Leftrightarrow t^2-4t+3-8=0\)
\(\Leftrightarrow t^2-4t-5=0\)
\(\Leftrightarrow\left(t-5\right)\left(t+1\right)=0\)
\(\Leftrightarrow[\dfrac{t-5=0\Leftrightarrow t=5\left(chọn\right)}{t+1=0\Leftrightarrow t=-1\left(loại\right)}\)
+5=\(\sqrt{4x-3}\)
\(\Leftrightarrow\)4x-3=25
\(\Leftrightarrow4x=28\)
\(\Leftrightarrow x=7\)
