Đặt \(\sqrt{2x+3}=t\ge0\Rightarrow2x=t^2-3\)
\(pt\Leftrightarrow\left(t^2-3\right)^2+12-4t^2+t=1\)
\(\Leftrightarrow t^4-10t^2+t+20=0\)
\(\Leftrightarrow\left(t^2-t-4\right)\left(t^2+t-5\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}t=\frac{1+\sqrt{17}}{2}\\t=\frac{-1+\sqrt{21}}{2}\end{cases}}\) \(\left(t\ge0\right)\)
\(\Rightarrow\hept{\begin{cases}x=\frac{3+\sqrt{17}}{4}\\x=\frac{5-\sqrt{21}}{4}\end{cases}}\)
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