Question

Решить уравнение
3^{x} +3^{3-x}-12=0

Answer 1

$3 {}^{x} + 3 {}^{3 - x} - 12 = 0 \\ 3 {}^{x} + \frac{27}{3 {}^{x} } - 12 = 0 \\ 3 {}^{x} = y \\ y + \frac{27}{y} - 12 = 0 \\ y {}^{2} - 12y + 27 = 0 \\ d = 144 - 4 \times 27 = 6 {}^{2} \\ y = \frac{12 + - 6}{2} \\ y = 3 \\ y = 9 \\ 1)3 {}^{x} =3 \\ x = 1 \\ 2)3 {}^{x} = 9 \\ x = 2$
Ответ: 1; 2