Question

Să se determine soluțiile reale ale ecuației [tex] 4^{x} -3* 2^{x}+2=0
[/tex]

Answer 1

$4^x-3*2^x+2=0 \\\\ 2^{2x}-3*2^x+2=0 \\\\ \underline{2^x\to t} \\\\\ t^2-3t+2=0 \\\\ \Delta=9-4*2 \to 1 \\\\\\ t_1= \frac{3+1}{2} \to 2 \\\\ t_2=\frac{3-1}{2} \to 1 \\\\\\ 2^x=2 \longrightarrow \boxed{x=1} \\\\\\ 2^x=1 \longrightarrow \boxed{x=0} \\\\\\ \boxed{\boxed{S_x \in \{0;1\} }}$