Решите уравнение, используя введение новой переменной: (x^2-7)^2-4(x^2-7)-45=0.

\[\left( x^{2} - 7 \right)^{2} - 4 \cdot \left( x^{2} - 7 \right) - 45 =\]

\[= 0\]

\[Пусть\ \left( x^{2} - 7 \right) = a:\]

\[a^{2} - 4a - 45 = 0\]

\[D = 4 + 45 = 49\]

\[a_{1} = 2 + 7 = 9;\ \ \ \]

\[a_{2} = a - 7 = - 5\]

\[Подставим:\]

\[x^{2} - 7 = 9\]

\[x^{2} = 16\]

\[x = \pm 4.\]

\[x^{2} - 7 = - 5\]

\[x^{2} = 2\]

\[x = \pm \sqrt{2}.\]

\[Ответ:\ \ x = \pm 4;\ \ x = \pm \sqrt{2}.\]