Question

me ajudem :( $2^{2x} - 3.2^{x}+2=0$

Answer 1

$2^{2x}-3\cdot2^{x}+2=0$

$(2^{x})^{2}-3\cdot2^{x}+2=0$

$\Delta=(-3)^2-4\cdot1\cdot2=9-8=1$

$2^{x}=\dfrac{-(-3)\pm\sqrt{1}}{2}=\dfrac{3\pm1}{2}$

$2^{x}=\dfrac{3+1}{2}=2~~\Rightarrow~~2^{x}=2~~\Rightarrow~~2^{x}=2^{1}~\Rightarrow~~\boxed{x=1}$

$2^{x}=\dfrac{3-1}{2}=1~~\Rightarrow~~2^{x}=1~~\Rightarrow~~2^{x}=2^{0}~~\Rightarrow~~\boxed{x=0}$

$S=\{0,1\}$