Решите уравнение: (x+2)(x+3)(x+4)(x+5)=24.

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

\[= 24\]

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

\[= 24\]

\[t = x^{2} + 7x + 10;\ \ \ \ t > 0\]

\[t(t + 2) - 24 = 0\]

\[t^{2} + 2t - 24 = 0\]

\[D = 2^{2} - 4 \cdot 1 \cdot ( - 24) =\]

\[= 4 + 96 = 100\]

\[t_{1} = \frac{- 2 + \sqrt{100}}{2} = \frac{- 2 + 10}{2} =\]

\[= \frac{8}{2} = 4\]

\[t_{2} = \frac{- 2 - \sqrt{100}}{2} = \frac{- 2 - 10}{2} =\]

\[= \frac{- 12}{2} = - 6\ (не\ подходит).\]

\[x^{2} + 7x + 10 = 4\]

\[x^{2} + 7x + 6 = 0\]

\[D = 7^{2} - 4 \cdot 1 \cdot 6 = 49 - 24 =\]

\[= 25\]

\[x_{1} = \frac{- 7 + \sqrt{25}}{2} = \frac{- 7 + 5}{2} =\]

\[= \frac{- 2}{2} = - 1\]

\[x_{2} = \frac{- 7 - \sqrt{25}}{2} = \frac{- 7 - 5}{2} =\]

\[= \frac{- 12}{2} = - 6\]

\[Ответ:\ - 1;\ - 6.\]