Đáp án:
\(\left[ \begin{array}{l}
x = 1 + \sqrt {21} \\
x = 1 - \sqrt {21}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left( {x - 5} \right)\left( {x + 1} \right)\left( {x - 3} \right)\left( {x + 3} \right) = 85\\
\to \left( {x - 5} \right)\left( {x + 3} \right)\left( {x + 1} \right)\left( {x - 3} \right) = 85\\
\to \left( {{x^2} - 2x - 15} \right)\left( {{x^2} - 2x - 3} \right) = 85\\
Đặt:{x^2} - 2x - 3 = t\\
\to {x^2} - 2x - 15 = t - 12\\
Pt \to t\left( {t - 12} \right) = 85\\
\to {t^2} - 12t - 85 = 0\\
\to \left[ \begin{array}{l}
t = 17\\
t = - 5
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^2} - 2x - 3 = 17\\
{x^2} - 2x - 3 = - 5\left( {vô nghiệm} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1 + \sqrt {21} \\
x = 1 - \sqrt {21}
\end{array} \right.
\end{array}\)
