6×4^x-13×6^x+6×9^x=0

Question

6×4^x-13×6^x+6×9^x=0

Answer 1

Делим на 6^х:
6× (2/3)^х -13 + 6× (3/2)^х = 0
Пусть (2/3)^х = а; 6 а + 6/а - 13 =0
6а^2 - 13 а + 6=0
D = 169 - 144 = 25
а = 3/2; (2/3)^х = 3/2; х = -1
а = 2/3; (2/3)^х = 2/3; х = 1
Ответ: -1; 1.

Answer 2

6•4^x-13•6^x+6•9^x=0 |:9^x>0

6•(4/9)^x-13•(6/9)^x+6=0

6•(2/3)^(2x)-13(2/3)^x+6=0
(2/3)^x=t>0

6•t²-13t+6=0
D=169-36•4=169-144=25=5²
t=(13±5)/12
t1=18/12=3/2
t2=8/12=2/3

1)(2/3)^x=2/3
x=1
2)(2/3)^x=3/2
(2/3)^x=(2/3)^(-1)
x=-1

ответ -1;1