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Rezolvati ecuatia 3^x+9^x=12

Răspuns :

3x+9x=12
12x=12
x=12:12
x=1
[tex]3^{x}+9^{x}=12\\ \text{Consideram functia}\ f:\mathbb{R}\rightarrow [0,\infty),f(x)=3^{x}+9^{x}\\ Pt. x\ \textgreater \ 1:\ 3^x+9^x\ \textgreater \ 3+9=12\Rightarrow f(x)\ \textgreater \ 12\\ Pt. x\ \textless \ 1:\ 3^x+9^x\ \textless \ 3+9=12\Rightarrow f(x)\ \textless \ 12\\ \text{Singura solutie este:}\ x=1[/tex]

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