a.
ĐKXĐ: \(x\ge-\dfrac{1}{3}\)
\(3x+1+\sqrt{3x+1}-8=0\)
Đặt \(\sqrt{3x+1}=t\ge0\)
\(\Rightarrow t^2+t-8=0\Rightarrow\left[{}\begin{matrix}t=\dfrac{-1+\sqrt{33}}{2}\\t=\dfrac{-1-\sqrt{33}}{2}< 0\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{3x+1}=\dfrac{-1+\sqrt{33}}{2}\)
\(\Rightarrow3x+1=\dfrac{17-\sqrt{33}}{2}\)
\(\Rightarrow x=\dfrac{15-\sqrt{33}}{6}\)
b.
\(2x^2+3x+9+\sqrt{2x^2+3x+9}-42=0\)
Đặt \(\sqrt{2x^2+3x+9}=t>0\)
\(\Rightarrow t^2+t-42=0\Rightarrow\left[{}\begin{matrix}t=6\\t=-7< 0\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{2x^2+3x+9}=6\)
\(\Leftrightarrow2x^2+3x+9=36\)
\(\Leftrightarrow2x^2+3x-27=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{9}{2}\end{matrix}\right.\)