Question

Решите уравнение пожалуйста

Answer 1

Объяснение:

$5 ^{2x} \times 5 = 25 + 74 \times {5}^{x } + 2 \times ( {5}^{x} )^{2} \\ ( {5}^{x} {)}^{2} \times 5 = 25 + 74 \times {5}^{x} + 2( {5}^{x} {)}^{2} \\ {t}^{2} \times 5 = 25 + 74t + {2t}^{2} \\ 5 {t}^{2} - 25 - 74t - 2 {t}^{2} = 0 \ \\\ 3 {t}^{2} + t - 75t - 25 = 0 \\ t(3t + 1) - 25(3t + 1) = 0 \\ (3t + 1) (t- 25) = 0 \\ \\ 3t + 1 = 0 \\ t = - \frac{1}{3} \\ \\ t = 25 \\ \\ {5}^{x} = 25 \\ {5}^{x} = {5}^{2} \\ x = 2$