4^ (x) + 12^ (x) = 2*36^ (x)

4^x + 12^x = 2*36^x / : 36^x

4^x/36^x + 12^x/36^x = 2

(4/36) ^x + (12/36) ^x - 2 = 0

(1/9) ^x + (1/3) ^x - 2 = 0

Пусть (1/3) ^x = t

t^2 + t - 2 = 0

D = 1 + 8 = 9

t1 = (- 1 + 3) / 2 = 1

t2 = (- 1 - 3) / 2 = - 2

Обратная замена

(1/3) ^x = 1

x = 0

(1/3) ^x = - 2

Нет решений

Ответ

0