Question

Sa se rezolve in R ecuatia 9 la puterea x + 3 la puterea x - 12=0

Answer 1

[tex]\displaystyle 9^x+3^x-12=0\\ \\ (3^x)^2+3^x-12=0\\ \\ \\ t=3^x\Rightarrow t^2+t-12=0\\ \\ \left \{ {{t_1+t_2=-1} \atop {t_1\times t_2=-12}} \right. \Leftrightarrow \left \{ {{t_1=3} \atop {t_2=-4}} \right. \\ \\ \\ Astfel:\\ \\ \left \{ {{3^x=3} \atop {3^x=-4}} \right. \Leftrightarrow \left \{ {{x=1} \atop {imposibil}} \right. \\ \\ \\ [/tex]