Question

$3^{x} + 3^{-x} = \frac{10}{3}$

Answer 1

$3^x+3^-^x= \frac{10}{3}$


$3^x+ \frac{1}{3^x}= \frac{10}{3}$

Notăm $3^x=t$

$t+ \frac{1}{t}= \frac{10}{3}$

aducem la acelasi numitor cu 3t

[tex]3t^2+3=10t 3t^2+3-10t=0 3t^2-10t+3=0 a=3 b=-10 c=3 delta=b^2-4ac = 100-36=64 x1=3 x2=1/3[/tex]

Revenim la substitutie

[tex]3^x=3 x=log_{3} 3=1 3^x= \frac{1}{3} x=log_{3} \frac{1}{3} =0-1=-1[/tex]