Question

решить уравнение 2^x*6^x=1/144 (1/5)^2x+3=5^x-2 (1/3)^2x+9(1/3)^x-162=0

Answer 1

2^x*6^x=1/144
12^x = 12^-2
x = -2
(1/5)^2x+3=5^x-2 | * 5^2x +3
1 = 5^3x+1
5^0 5^3x+1
3x +1 = 0
x = -1/3
(1/3)^2x+9(1/3)^x-162=0
(1/3)^x =t
t² +9t -162 = 0
по т. Виета корни -18  и  9
а) t = -18
(1/3)^x = -18
∅
б) (1/3)^x = 9
x = -2