Question

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数Ⅱの問題です
証明の仕方がよく分かりません

39 次の3次方程式を解け｡
(1) x³=8
(2) x³ = -1

Answer 1

らら

(1)x^3=8
x^3-(2)^3=0
(x-2)(x^2+2x+4)=0
(x+1)^2-1+4=0
(x+1)^2=-3
x+1=±√3i
x=-1±√3i
∴x=2,-1±√3i
(2)x^3=-1
x^3+1^3=0
(x+1)(x^2-x+1)=0
x^2-x+1=0
x=1/2±√3i/2
∴x=-1,1/2±√3i/2