Question

conta completa da equação 2^2x-5.2^x+4=0

Answer 1

$2^{2x}-5\cdot2^x+4=0\\ (2^x)^2-5\cdot2^x+4=0\\\\ 2^x=y\\\\ (y)^2-5(y)+4=0\\\\ \Delta =b^2-4ac\\ \Delta=(-5)^2-4\cdot1\cdot4\\ \Delta=25-16\\ \Delta=9\\\\ y= \dfrac{-b\pm \sqrt{\Delta} }{2a} = \dfrac{-(-5)\pm \sqrt{9} }{2\cdot1}= \dfrac{5\pm3}{2}\begin{cases}y_1=1\\ y_2=4\end{cases}\\\\\\ 2^x=y,~lembra????\\\\ 2^x=1\\ \not2^x=\not2^0\\\\ x_1=0\\\\\\ 2^x=4\\ \not2^x=\not2^2 \\ x_2=2\\\\\\ \Large\boxed{\text{S}=\{0,2\}}$