Question

ALGUM ANJO DA MATEMATICA ME AJUDA PFVR! 6

Calcular a solução da equação x² – 5x + 40 = 0, considerando o conjunto dos números complexos.

Answer 1

Resposta:

$x_{1}=\frac{5+3\sqrt{15}i}{2}\ e\ x_{2}=\frac{5-\sqrt{15}i}{2}$

Explicação passo a passo:

$x^2-5x+40=0\\\\a=1,\ b=-5\ e\ c=40\\\\x_{1,2}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\x_{1,2}=\frac{-(-5)\±\sqrt{(-5)^2-4(1)(40)}}{2(1)}\\\\x_{1,2}=\frac{5\±\sqrt{25-160}}{2}\\\\x_{1,2}=\frac{5\±\sqrt{-135}}{2}\\\\x_{1,2}=\frac{5\±\sqrt{135}i}{2}\\\\x_{1,2}=\frac{5\±\sqrt{3^2\bullet15}i}{2}\\\\x_{1,2}=\frac{5\±3\sqrt{15}i}{2}\\\\x_{1}=\frac{5+3\sqrt{15}i}{2}\ e\ x_{2}=\frac{5-\sqrt{15}i}{2}$