Question

va rog ajutor la ex asta

Answer 1

[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]