ĐKXĐ: \(\left\{{}\begin{matrix}3x^2+5x+1>=0\\3x^2+5x-7>=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>=\dfrac{-5+\sqrt{13}}{6}\\x< =\dfrac{-5-\sqrt{13}}{6}\end{matrix}\right.\\\left[{}\begin{matrix}x>=\dfrac{-5+\sqrt{109}}{6}\\x< =\dfrac{-5-\sqrt{109}}{6}\end{matrix}\right.\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x< =\dfrac{-5-\sqrt{109}}{6}\\x>=\dfrac{-5+\sqrt{109}}{6}\end{matrix}\right.\)
\(\sqrt{3x^2+5x+1}-\sqrt{3x^2+5x-7}=2\)
=>\(\sqrt{3x^2+5x+1}-3-\sqrt{3x^2+5x-7}+1=0\)
=>\(\dfrac{3x^2+5x+1-9}{\sqrt{3x^2+5x+1}+3}-\dfrac{3x^2+5x-7-1}{\sqrt{3x^2+5x-7}+1}=0\)
=>\(3x^2+5x-8=0\)
=>\(\left(3x+8\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}x=1\left(nhận\right)\\x=-\dfrac{8}{3}\left(nhận\right)\end{matrix}\right.\)