Question

R,$3^{x+1} + 3^{1-x}=10$

Answer 1

3^(x+1)+3^(1-x)=10 <=> 3*3^x+3/3^x>=10 ...(*)
Notam t=3^x>0 si obtinem (*) <=> 3t+3/t>=10 <=> 3t^2+3>=10t <=> 3t^2-10t+3>=0
delta=(-10)^2-4*3*3=100-24=76
t1,2=(10+-rad(76))/6=(10+-2rad(19))/6=(5+-rad(19))/3

t=(5+rad(19))/3 <=> 3^x=(5+rad(19))/3 <=> x=log in baza 3 din (5+rad(19))/3.
t=(t-rad(19))/3 <=> 3^x=(5-rad(19))/3 <=> x=log in baza 3 din (5-rad(19))/3.