Question

cum se rezolva :  3 la puterea x + 3 la puterea -x = 10/3 

Answer 1

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

Notam $3^x=a>0$ si aducem la acelasi numitor:

$a+\dfrac1a=\dfrac{10}{3}\Rightarrow 3a^2-10a+3=0\Rightarrow a_{1;2}=\dfrac{10\pm8}{6}$

$a_1=3;\ \ \ a_2=\dfrac13=3^{-1}$

$3^x=3\Rightarrow x=1;\ \ \ 3^x=3^{-1}\Rightarrow x=-1$