Question

A soma das raízes da equação
$2 ^{2 \times } = 5.2 ^{ \times } - 4$
é ?

Answer 1

Olá, bom dia!

$2^{2x}=5\cdot2^x-4\\2^x\cdot2^x=5\cdot2^x-4\\\\2^x=y\\\\y\cdot y=5y-4\\y^2-5y+4=0\\\\Coeficientes:\;a=1,\;b=-5,\;e\;c=4\\\\\Delta=b^2-4ac\\\Delta=(-5)^2-4\cdot1\cdot4\\\Delta=25-16\\\Delta=9\\\\y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\y=\dfrac{-(-5)\pm\sqrt{9}}{2\cdot1}\\\\y=\dfrac{5\pm3}{2}\\\\y_1=\dfrac{5+3}{2}=\dfrac{8}{2}=4\\\\y_2=\dfrac{5-3}{2}=\dfrac{2}{2}=1\\\\Terminou?\;N\~ao.\\\\2^x=y\\2^x=4\\2^x=2^2\\x_1=2\\\\2^x=1\\2^x=2^0\\x_2=0\\\\S={0,\;2}$


Espero ter ajudado.
Bons estudos! :)