Question

ALGUM ANJO DA MATEMATICA ME AJUDA PFVR! 4

Calcular a solução da equação x² + 80 = 0, considerando o conjunto dos números complexos.

Answer 1

Resposta:

$x=4\sqrt{5}i,\ x=-4\sqrt{5}i$

Explicação passo a passo:

$x^2+80=0\\\\a=1,\ b=0\ e\ c=80\\\\x_{1,2}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\x_{1,2}=\frac{-0\±\sqrt{0^2-4(1)(80)}}{2(1)}\\\\x_{1,2}=\frac{0\±\sqrt{0-320}}{2}\\\\x_{1,2}=\±\frac{\sqrt{320}i}{2}\\\\x_{1,2}=\±\frac{\sqrt{2\bullet2\bullet2\bullet2\bullet2\bullet2\bullet5}i}{2}\\\\x_{1,2}=\±\frac{\sqrt{2^2\bullet2^2\bullet2^2\bullet5}i}{2}\\\\x_{1,2}=\±\frac{2\bullet2\bullet2\sqrt{5}i}{2}\\\\x_{1,2}=\±\frac{8\sqrt{5}i}{2}\\\\x_{1,2}=\±4\sqrt{5}i\\\\x_{1}=4\sqrt{5}i\ e\ x_{2}=-4\sqrt{5}i$

$ou\\\\\\x^2+80=0\\\\x^2=-80\\\\\sqrt{x^2}=\sqrt{-80}\\\\x=\±\sqrt{80}i\\\\x=\±\sqrt{2\bullet2\bullet2\bullet2\bullet5}i\\\\x=\±2\bullet2\sqrt{5}i\\\\x=\±4\sqrt{5}i\\\\x=4\sqrt{5}i,\ x=-4\sqrt{5}i$