Question

2^2x - 3.2^x -6=-8 resposta

Answer 1

Oi Suely,

aplique as propriedades da exponenciação..

$2^{2x}-3\cdot2^x-6=-8\\(2^x)^2-3\cdot(2^x)-6+8=0\\\\\large\boxed{\overbrace{\underbrace{2^x=y}}}\\\\\\y^2-3y+2=0\\\\\Delta=(-3)^2-4\cdot1\cdot2\\\Delta=9-8\\\Delta=1\\\\y= \dfrac{-(-3)\pm \sqrt{1} }{2\cdot1} = \dfrac{3\pm1}{2} \begin{cases}y_1= \dfrac{3-1}{2}= \dfrac{2}{2}=1\\\\y_2= \dfrac{3+1}{2}= \dfrac{4}{2}=2    \end{cases}\\\\\\\large\boxed{\underbrace{\overbrace{2^x=y}}}$

$2^x=1~~~~~~~~~~~~~~~~~~~~~2^x=2\\2^x=2^0~~~~~~~~~~~~~~~~~~~~2^x=2^1\\\not2^x=\not2^0~~~~~~~~~~~~~~~~~~\not2^x=\not2^1~\\\\x_1=0~~~~~~~~~~~~~~~~~~~~~~x_2=1$


$\boxed{\huge\boxed{\text{S}=\{0,1\}}}}}$


Tenha ótimos estudos :))