Question

Giải PT : \(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x\ge-\frac{1}{3}\\x\ne0\end{matrix}\right.\)

\(\Leftrightarrow12x^2-3x-1-4x\sqrt{3x+1}=0\)

Đặt \(\sqrt{3x+1}=a\)

\(\Rightarrow12x^2-4xa-a^2=0\)

\(\Leftrightarrow\left(6x+a\right)\left(2x-a\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=-6x\\a=2x\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\sqrt{3x+1}=-6x\left(x\le0\right)\\\sqrt{3x+1}=2x\left(x\ge0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=36x^2\\3x+1=4x^2\end{matrix}\right.\) (casio)