27 tháng 12 2019 lúc 20:45
ĐKXĐ:...
\(\Leftrightarrow4x^2-5x+1=-2\sqrt{x-1}\)
\(\Leftrightarrow3x^2-3x+x^2-2x+1=-2\sqrt{x-1}\)
\(\Leftrightarrow3x\left(x-1\right)+\left(x-1\right)^2=-2\sqrt{x-1}\)
Đặt \(\sqrt{x-1}=t\left(t\ge0\right)\Rightarrow t^2=x-1\Leftrightarrow x=t^2+1\)
\(\Leftrightarrow3\left(t^2+1\right)t^2+t^4=-2t\)
\(\Leftrightarrow3t^4+3t^2+t^4+2t=0\)
\(\Leftrightarrow4t^4+3t^2+2t=0\)
\(\Leftrightarrow t\left(4t^3+3t+2\right)=0\Leftrightarrow\left[{}\begin{matrix}t=0\\t=-\frac{1}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow t=0\Leftrightarrow x=1\left(tm\right)\)
Vậy x=1
