x³=a 设b^3=a,则b是a的实数立方根.
x³-b³=0
(x-b)(x²+bx+b²)=0
x1=b
x²+bx+b²=0
x²+bx+(b/2)²-b²/4+b²=0
(x+b/2)²+3b²/4=0
(x+b/2)²-(√3ib/2)²=0
x2=-(1+√3i)b/2
x3=-(1-√3i)b/2
x³=a 设b^3=a,则b是a的实数立方根.
x³-b³=0
(x-b)(x²+bx+b²)=0
x1=b
x²+bx+b²=0
x²+bx+(b/2)²-b²/4+b²=0
(x+b/2)²+3b²/4=0
(x+b/2)²-(√3ib/2)²=0
x2=-(1+√3i)b/2
x3=-(1-√3i)b/2