Question

Решите на множестве R уравнения

Answer 1

Ответ:

$3 \times {25}^{x} - 2 \times {5}^{x} = 1 \\ 3 \times {5}^{2x} - 2 \times {5}^{x} - 1 = 0 \\ {5}^{x} = y \\ 3 {y}^{2} - 2y - 1 = 0 \\ d = 4 + 12 = 16 \\ y1 = \frac{2 + 4}{6} = 1 \\ y2 = \frac{2 - 4}{6} = - \frac{1}{3} \\ {5}^{x} = 1 \\ {5}^{x} = {5}^{0} \\ x = 0$