Question

equação exponencial 2 (x + 1) . 2 (x + 3) = 16

Answer 1

Resposta:

$\boxed{S'=\{x^2+4x-1\}}\\\boxed{S''=\{\dfrac{-4+\sqrt{20}}{2};\dfrac{-4-\sqrt{20}}{2}\}}$

Explicação passo-a-passo:

$2^{(x+1)} . 2^{(x+3)} = 16\\2^{(x+1)} . 2^{(x+3)} = 2^4\\{(x+1)} . {(x+3)} = 4\\x^2+3x+x+3=4\\x^2+4x-1=0$

Solução da equação do 2º grau por Fórmula Resolutiva:

$x=\dfrac{-b\±\sqrt{b^2-4.a.c}}{2.a}\\x=\dfrac{-4\±\sqrt{4^2-4.1.(-1)}}{2.1}\\x=\dfrac{-4\±\sqrt{16+4}}{2}\\x=\dfrac{-4\±\sqrt{20}}{2}\\x'=\dfrac{-4+\sqrt{20}}{2}\\x''=\dfrac{-4-\sqrt{20}}{2}\\\\\boxed{S=\{\dfrac{-4+\sqrt{20}}{2};\dfrac{-4-\sqrt{20}}{2}\}}$