Question

\(\sqrt{x+3}\) + \(\sqrt{2x-1}\) = \(3\sqrt{3x-2}\)

Answer 1

ĐKXĐ: \(x\ge\dfrac{1}{2}\)

\(pt\Leftrightarrow3x+2+2\sqrt{\left(x+3\right)\left(2x-1\right)}=9\left(3x-2\right)\)

\(\Leftrightarrow2\sqrt{\left(x+3\right)\left(2x-1\right)}=24x-20\)

\(\Leftrightarrow\sqrt{2x^2+5x-3}=12x-10\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x^2+5x-3=144x^2+100-240x\\12x-10\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)\left(142x-103\right)=0\\x\ge\dfrac{5}{6}\end{matrix}\right.\)

\(\Leftrightarrow x=1\left(tm\right)\)