Question

qual a resposta para 4^(x+1)-9.2^(x)+2=0

Answer 1

Resposta:

S={-2,1}

Explicação passo-a-passo:

$4^{x+1}-9.2^x+2=0\\ \\ (2^2)^{x+1}-9.2^x+2=0\\ \\ 2^{2x+2}-9.2^x+2=0\\ \\ 2^{2x}.2^2-9.2^x+2=0\\ \\ (2^x)^2.4-9.2^x+2=0\\ \\ coloca~~2^x=y\\ \\ 4y^2-9y+2=0$

a=4

b=-9

c=2

Δ=b²-4ac

Δ=(-9)²-4(4)(2)

Δ=81-32

Δ=49

$y={-b\pm\sqrt{\Delta} \over2a}={-(-9)\pm\sqrt{49} \over2.(4)}={9\pm7\over8}\\ \\ y_1={9+7\over8}={16\over8}=2\\ \\ y_2={9-7\over8}={2\over8}={1\over4}$

$Se~~2^x=y\\ p/y=2\\ 2^x=2\\ x=1\\ \\ p/y={1\over4}\\ \\ 2^x={1\over4}\\ \\ 2^x={1\over2^2}\\ \\ 2^x=2^{-2}\\ \\ x=-2$