Question

A solução da equação 2^2+2x-9.2^x+2=0 é:

Answer 1

$2^{2+2x}-9\cdot2^x+2=0\\ 2^2\cdot2^{2x}-9\cdot2^x+2=0\\ 4\cdot(2^x)^2-9\cdot2^x+2=0\\\\ 2^x=y\\\\ 4y^2-9y+2=0\\\\ y_1= \dfrac{1}{8} ~~e~~y_2=2\\\\\\ 2^x=y:$

$2^x= \dfrac{1}{8}~~~~~~~~~~~~~~~~~2^x=2\\\\ 2^x= \dfrac{1}{2^3}~~~~~~~~~~~~~~~~\not2^x=\not2^1\\\\ \not2^x=\not2^{-3}~~~~~~~~~~~~~~~~~~~x_2=1\\\\ x_1=-3\\\\\\ \boxed{S=\left\{-3,1\} }$