Question

Calcule as raízes da seguinte equação cúbica: x³-6​

Answer 1

Resposta:

Explicação passo a passo:

Answer 2

Resposta:

$S=\{\sqrt[3]{6},~~\sqrt[3]{6}(-\frac{1}{2}+\frac{\sqrt{3} }{2}i),~~\sqrt[3]{6}(-\frac{1}{2} -\frac{\sqrt{3} }{2}i)$

Explicação passo a passo:

Resolva a equação:

x³ - 6 = 0

x³ = 6

x = ∛6

Seja Z = 6

|Z| = 6 ⇒ α = 0

$Z_k= \sqrt[n]{|Z|} (cos\frac{\alpha +2k\pi }{n}+i.sen\frac{\alpha +2k\pi }{3} )\\\\k={0,1,2}\\\\Z_0=\sqrt[3]{6}(cos\frac{0+2.0.\pi }{3} +i.sen\frac{0+2.0.\pi }{3})\\\\Z_0=\sqrt[3]{6} (cos0+isen0)\\\\Z_0=\sqrt[3]{6}(1+0)\\\\Z_0=\sqrt[3]{6} \\\\Z_1= \sqrt[3]{6}(cos\frac{0+2.1.\pi }{3} +i.sen\frac{0+2.1.\pi }{3})\\\\Z_1=\sqrt[3]{6} (cos\frac{2\pi }{3} +i.sen\frac{2\pi }{3})\\\\Z_1=\sqrt[3]{6}(-\frac{1}{2}+\frac{\sqrt{3} }{2}i )\\\\Z_2= \sqrt[3]{6}(cos\frac{0+2.2.\pi }{3} +i.sen\frac{0+2.2\pi }{3})$

$Z_2=\sqrt[3]{6}(cos\frac{4\pi }{3}+i.sen\frac{4\pi }{3} )\\\\Z_2=\sqrt[3]{6} (-\frac{1}{2 }-\frac{3}{2}i)$