第1个回答 2013-04-08
(1)x³-27=0
(x-3)(x²+3x+9)=0
由x=[-3±√(3²-4×9)]/2
=(-3±3√3i)/2
∴x1=3, x2,3=(-3±3√3i)
(2)64x³+125=0
(4x)³+5³=0
(4x+5)(16x²-20x+25)=0
由x=[20±√(400-4×16×25)]/2
=(20±20√3i)/2
=10±10√3i
∴x1=-5/4, x2,3=10±10√3i
(3)(x/2)³=-125
x³+100=0
(x+10)(x²-10x+100)=0
由x=[10±√(100-400)/2
=5±5√3i
∴x1=-10, x2,3=5±√3i.
(4)(x-1)³-216=0
(x-1-6)(x2-2x+1+6x-6+36)=0
(x-7)(x²+4x+31)=0
x=-2±6√3i
∴x1=7, x2,3=-2±6√3i.本回答被提问者采纳