Question

Решите уровнение, 70 баллов!

Answer 1

Ответ:

$5 \times {4}^{ {x}^{2} + 4x} + 20 \times {10}^{ {x}^{2} + 4x - 1 } - 7 \times {25}^{ {x}^{2} + 4x } = 0 \\ 5 \times {2}^{2( {x}^{2} + 4x)} + 20 \times \frac{1}{10} \times {2}^{ {x}^{2} + 4x} \times {5}^{ {x}^{2} + 4x} - 7 \times {5}^{2( {x}^{2} + 4x)} = 0 \\ | \div (2 \times 5) {}^{x {}^{2} + 4x } \\ 5 \times \frac{ {2}^{ {x}^{2} + 4x } }{ {5}^{ {x}^{2} + 4x } } + 2 - 7 \times \frac{ {5}^{ {x}^{2} + 4x} }{ {2}^{ {x}^{2} + 4x } } = 0 \\ \\ ( \frac{2}{5} ) {}^{ {x}^{2} + 4 x} = t \\ t > 0 \\ \\ 5t + 2 - \frac{7}{t} = 0 \\ 5 {t}^{2} + 2 t - 7 = 0 \\ D = 4 + 140 = 144 \\ t_1 = \frac{ - 2 + 12}{10} = 1 \\ t_2 = - 1.4$

второй корень не подходит

$( \frac{2}{5} ) {}^{ {x}^{2} + 4x} = 1 \\ {x}^{2} + 4x = 0 \\ x(x + 4) = 0 \\ x_1 = 0 \\ x_2 = - 4$

Ответ: -4; 0