Question

Ecuația 9^x+3^x-12=0 cum se face ?

Answer 1

[tex]9^x+3^x-12=0\\ (3^x)^2+3^x-12=0\\ Notam\ 3^x=t,t\ \textgreater \ 0,iar\ ecuatia\ devine:\\ t^2+t-12=0\\ \Delta=1+4\cdot 12=49\Rightarrow \sqrt{\Delta}=7\\ t_1=\frac{-1+7}{2}=3\\ t_2=\frac{-1-7}{2}=-4\\ i)3^x=3\Rightarrow x=1\\ ii)3^x=-4,imposibil.\\ S:x=1[/tex]

Answer 2

3^x=u
u²+u-12=0

u1,2=(-1+-√49)/2
u1=-4  3^x=-4 x∉R
u2=3  3^x=3 x=1 solutie unica