Question

a soma das raízes da equação é

Answer 1

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$2^{2x+1}-2^{x+4}=2^{x+2}-32 \\ \\ (2^x)^2.2^1-2^x.2^4=2^x.2^2-32 \\ \\ 2^x=y \\ \\2 y^2-16y=4y-32 \\ \\2 y^2-20y+32=0~~~\div~por~~2 \\ \\ y^2-10y+16=0 \\ \\ \triangle=10^2-64=100-64=36 \\ \\ y= \frac{10\pm6}{2} \\ \\ y'= \frac{16}{2} =8~~~~~~~~~~~~y"= \frac{4}{2} =2 \\ \\ se \\ 2^x=y \\ 2^x=8~~~~~~~~~~~2^x=2 \\ 2^x=2^3~~~~~~~~~~~~x=1 \\ x=3 \\ \\ Soma=3+1=4$