[tex]4^x-9\cdot2^x+8 = 0
\\2^{2x}-9\cdot2^x+8 = 0
\\\text{Notam }2^x = t \ \textgreater \ 0
\\t^2-9t+8=0
\\\Delta = 81-32 = 49
\\t_{1} = \frac{9+7}{2} = 8 \ \textgreater \ 0 \text{ (e ok).}
\\t_{2} = \frac{9-7}{2} = 1 \ \textgreater \ 0 \text{ (e ok).}
\\ 1. t=8 \Rightarrow2^x=8\Rightarrow x=3
\\ 2.t=1 \Rightarrow2^x=1\Rightarrow x=0
\\\Rightarrow x\in\{0,3\}
[/tex]
