Giải thích các bước giải:
\(\begin{array}{l}
\sqrt {x - 1} + \sqrt {x + 7} + {x^2} - 3x - 2 = 0(*)\\
Dk:x \ge 1\\
(*) \Leftrightarrow (\sqrt {x - 1} - 1) + (\sqrt {x + 7} - 3) + {x^2} - 3x + 2 = 0\\
\Leftrightarrow \frac{{x - 2}}{{\sqrt {x - 1} + 1}} + \frac{{x - 2}}{{\sqrt {x + 7} + 3}} + (x - 2)(x - 1) = 0\\
\Leftrightarrow (x - 2)\left( {\frac{1}{{\sqrt {x - 1} + 1}} + \frac{1}{{\sqrt {x + 7} + 3}} + x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2 \to Tm\\
\frac{1}{{\sqrt {x - 1} + 1}} + \frac{1}{{\sqrt {x + 7} + 3}} + x - 1 = 0(**)
\end{array} \right.\\
Ta\;co:\frac{1}{{\sqrt {x - 1} + 1}} > 0;\frac{1}{{\sqrt {x + 7} + 3}} > 0;x - 1 \ge \forall x \ge 1\\
\Rightarrow (**)\;vo\;nghiem\\
Vay\;nghiem\;pt\;la\;x = 2
\end{array}\)
