Решите уравнение: (x-3)(x-2)(x+4)(x+5)=60.

\[(x - 3)(x - 2)(x + 4)(x + 5) =\]

\[= 60\]

\[(x - 3)(x + 5)(x - 2)(x + 4) =\]

\[= 60\]

\[\left( x^{2} + 2x - 15 \right)\left( x^{2} + 2x - 8 \right) - 60 = 0\]

\[t = x^{2} + 2x - 8\]

\[(t - 7)t - 60 = 0\]

\[t^{2} - 7t - 60 = 0\]

\[D = \text{(} - 7)² - 4 \cdot 1 \cdot ( - 60) =\]

\[= 49 + 240 = 289\]

\[t_{1} = \frac{7 + \sqrt{289}}{2} = \frac{7 + 17}{2} = \frac{24}{2} =\]

\[= 12\]

\[t_{2} = \frac{7 - \sqrt{289}}{2} = \frac{7 - 17}{2} =\]

\[= \frac{- 10}{2} = - 5\]

\[1)\ x^{2} + 2x - 8 = 12\]

\[x^{2} + 2x - 20 = 0\]

\[D = 2^{2} - 4 \cdot 1 \cdot ( - 20) =\]

\[= 4 + 80 = 84\]

\[x_{1}\frac{- 2 + \sqrt{84}}{2} = \frac{- 2 + 2\sqrt{21}}{2} =\]

\[= - 1 + \sqrt{21}\]

\[x_{2} = \frac{- 2 - \sqrt{84}}{2} = \frac{- 2 - 2\sqrt{21}}{2} =\]

\[= - 1 - \sqrt{21}\]

\[2)\ x^{2} + 2x - 8 = - 5\]

\[x^{2} + 2x - 3 = 0\]

\[D = 2^{2} - 4 \cdot 1 \cdot ( - 3) = 4 + 12 =\]

\[= 16\]

\[x_{1} = \frac{- 2 + \sqrt{16}}{2} = \frac{- 2 + 4}{2} = \frac{2}{2} =\]

\[= 1\]

\[x_{2} = \frac{- 2 - \sqrt{16}}{2} = \frac{- 2 - 4}{2} =\]

\[= \frac{- 6}{2} = - 3\]

\[Ответ:\ - 1 + \sqrt{21};\ \ - 1 - \sqrt{21};\ \]

\[\ 1;\ - 3.\]