Решите уравнение методом замены переменной: (x^2+x+1)(x^2+x+2)=12.

\[\left( x^{2} + x + 1 \right)\left( x^{2} + x + 2 \right) = 12\]

\[Пусть\ t = x^{2} + x + 1:\text{\ }\]

\[t(t + 1) = 12\]

\[t^{2} + t - 12 = 0\]

\[t_{1} + t_{2} = - 1\]

\[t_{1} \cdot t_{2} = - 12\]

\[\Longrightarrow t_{1} = - 4,\ \ t_{2} = 3.\]

\[Ответ:\ x = - 2;x = 1.\]