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\[\begin{array}{l}
\sqrt {4{x^2} + x + 6} = 4x - 2 + 7\sqrt {x + 1} \\
\Leftrightarrow \sqrt {4{x^2} + x + 6} - 3\sqrt {x + 1} = 2(2x - 1 + 2\sqrt {x + 1} )
\end{array}\]
Liên hợp: \[\begin{array}{l}
\frac{{4{x^2} - 8x - 3}}{{\sqrt {4{x^2} + x + 6} + 3\sqrt {x + 1} }} = 2\frac{{4{x^2} - 8x - 3}}{{2x - 1 - 2\sqrt {x + 1} }}\\
\Rightarrow \left[ \begin{array}{l}
4{x^2} - 8x - 3 = 0\\
\frac{1}{{\sqrt {4{x^2} + x + 6} + 3\sqrt {x + 1} }} - \frac{2}{{2x - 1 - 2\sqrt {x + 1} }} = 0
\end{array} \right.
\end{array}\]
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