Đáp án: $x = - 0,36;x = - 4,63$
Giải thích các bước giải:
$\begin{array}{l}
\left( {x + 1} \right)\left( {x + 2} \right)\left( {x + 3} \right)\left( {x + 4} \right) = 10\\
\Leftrightarrow \left( {x + 1} \right)\left( {x + 4} \right)\left( {x + 2} \right)\left( {x + 3} \right) = 10\\
\Leftrightarrow \left( {{x^2} + 5x + 4} \right)\left( {{x^2} + 5x + 6} \right) = 10\\
Dat:\left( {{x^2} + 5x + 4} \right) = t\\
\Leftrightarrow t\left( {t + 2} \right) = 10\\
\Leftrightarrow {t^2} + 2t - 10 = 0\\
\Leftrightarrow {t^2} + 2t + 1 = 11\\
\Leftrightarrow {\left( {t + 1} \right)^2} = 11\\
\Leftrightarrow \left[ \begin{array}{l}
t + 1 + \sqrt {11} = 0\\
t + 1 - \sqrt {11} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
{x^2} + 5x + 4 + 1 + \sqrt {11} = 0\left( {vn} \right)\\
{x^2} + 5x + 4 + 1 - \sqrt {11} = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 0,36\\
x = - 4,63
\end{array} \right.\\
Vậy\,x = - 0,36;x = - 4,63
\end{array}$
