Решите уравнение методом замены переменной: (x+5)^4-10(x+5)^2+9=0.

\[(x + 5)^{4} - 10 \cdot (x + 5)^{2} + 9 = 0\]

\[Пусть\ t = (x + 5)^{2}:\]

\[t^{2} - 10t + 9 = 0\]

\[t_{1} + t_{2} = 10\]

\[t_{1} \cdot t_{2} = 9\]

\[\Longrightarrow t_{1} = 9,\ \ t_{2} = 1.\]

\[Ответ:\ x = - 2;\ x = - 8;\ \]

\[x = - 4;\ x = - 6.\]