Question

помогите решить 1 уравнение

Answer 1

(2/3)^(2x) + (3/4)*[(2/3)^x)] - (27/4) = 0
(2/3)^x = z, z > 0
z² + (3/4)*z - 27/4 = 0     умножаем на 4
4z² + 3z - 27 = 0
D = 9 + 4*4*27 = 9 + 432 = 441
z₁ = (-3 - 21)/8
z₁ = - 3< 0, не удовлетворяет условию: z > 0
z₂ = (- 3 + 21)/8
z₂ =(3/2)^2
(2/3)^x =(3/2)^2
(2/3)^x = (2/3)^(-2)
x = - 2
Ответ: х = - 2