Помогите решить 5^(x+1)+3*5^-x=16

Question

Помогите решить
5^(x+1)+3*5^-x=16

Answer 1

(5^x)*5 + 3*(1/5^x) - 16 = 0   / *5^x
5*(5^2x)  - 16*(5^x) + 3 = 0
5^x = t
 5*(t^2) - 16t + 3 = 0
D = 256 - 4*5*3 = 196
t1 = (16 - 14)/10
t1 = 1/5
t2 = (16 + 14)/10
t2 = 3
5^x = 1/5
5^x = 5^(- 1)
x1 = - 1
5^x = 3
x2 = log(5)  3