Question

Решить уравнение
$3^{ x+1} + 3 * 3^{x-1} - 3^{x} - 9 = 0$

Answer 1

${3}^{x + 1} + 3 \times {3}^{x - 1} - {3}^{x} - 9 = 0$

${3}^{x} \times 3 + 3 \times {3}^{x} \times \frac{1}{3} - {3}^{x} - 9 = 0$

Пусть 3ˣ = t :

$3t + 3 \times \frac{1}{3} t - t - 9 = 0$

$3t + t - t - 9 = 0$

$3t - 9 = 0$

$3t = 9$

$t = 3$

${3}^{x} = 1$

$x = 1$

Ответ : х = 1