3*9^х-5*6^х+2*4^х=0 показательное

Question

3*9^х-5*6^х+2*4^х=0 показательное

Answer 1

3·3^2x -5· 2^x·3^x + 2·2^2x = 0 | : 2^2x
3·(3/2)2x -5·(3/2)^x + 2 = 0
(3/2)^x = t
3t² - 5t +2 = 0
D = 1
t = 1  и  t = 4/6=2/3
а) t = 1
(3/2)^x = 1
x = 0
б) (3/2)^x = 2/3
x = -1