Giải thích các bước giải:
\(\begin{array}{l}
a.t = {x^2} + x\left( {t > 0} \right)\\
Pt \to {t^2} + 4t - 12 = 0\\
\to \left( {t - 2} \right)\left( {t + 6} \right) = 0\\
\to \left[ \begin{array}{l}
t = 2\\
t = - 6\left( l \right)
\end{array} \right. \to {x^2} + x = 2 \to \left[ \begin{array}{l}
x = 1\\
x = - 2
\end{array} \right.\\
b.t = {x^2} + 2x + 3\left( {t > 0} \right)\\
Pt \to {t^2} - 9t + 18 = 0\\
\to \left( {t - 6} \right)\left( {t - 3} \right) = 0\\
\to \left[ \begin{array}{l}
t = 6\\
t = 3
\end{array} \right. \to \left[ \begin{array}{l}
{x^2} + 2x + 3 = 6\\
{x^2} + 2x + 3 = 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left( {x - 1} \right)\left( {x + 3} \right) = 0\\
x\left( {x + 2} \right) = 0
\end{array} \right. \to \left[ \begin{array}{l}
x = 1\\
x = - 3\\
x = 0\\
x = - 2
\end{array} \right.\\
c.\left( {{x^2} - 4} \right)\left( {{x^2} - 10} \right) = 72\\
\to {x^4} - 14{x^2} - 32 = 0\\
t = {x^2}\left( {t > 0} \right)\\
Pt \to {t^2} - 14t - 32 = 0\\
\to \left[ \begin{array}{l}
t = 16\\
t = - 2\left( l \right)
\end{array} \right. \to {x^2} = 16\\
\to \left[ \begin{array}{l}
x = 4\\
x = - 4
\end{array} \right.\\
d.\left( {{x^2} + x} \right)\left( {{x^2} + x + 1} \right) = 42\\
t = {x^2} + x\left( {t > 0} \right)\\
Pt \to t\left( {t + 1} \right) = 42\\
\to {t^2} + t - 42 = 0\\
\to \left[ \begin{array}{l}
t = 6\\
t = - 7\left( l \right)
\end{array} \right. \to {x^2} + x = 6\\
\to \left[ \begin{array}{l}
x = 2\\
x = - 3
\end{array} \right.\\
e.\left( {x - 1} \right)\left( {x + 5} \right)\left( {x - 3} \right)\left( {x + 7} \right) - 297 = 0\\
\to \left( {{x^2} + 4x - 5} \right)\left( {{x^2} + 4x - 21} \right) - 297 = 0\\
t = {x^2} + 4x - 5\left( {t > 0} \right)\\
Pt \to t\left( {t - 16} \right) - 297 = 0\\
\to {t^2} - 16t - 297 = 0\\
\to \left[ \begin{array}{l}
t = 27\\
t = - 11\left( l \right)
\end{array} \right. \to {x^2} + 4x - 5 = 27\\
\to \left[ \begin{array}{l}
x = 4\\
x = - 8
\end{array} \right.
\end{array}\)
