看情况,是要实根还是虚根,
若是实根,直接开方,因为3^3=27,4^3=64,5^3=125,6^3=216
所以:
(1)64x^3=125,
x^3=125/64
x=5/4
(2)(x-1)^3=-216
x-1=-6
x=-5
若是虚根:
先分解因式
x^3+y^3=(x+y)*(x^2-xy+y^2)
x^3-y^3=(x-y)*(x^2+xy+y^2)
(1)64x^3-125=(4x-5)*(16x^2+20x+25)=0
4x-5=0or16x^2+20x+25=0
x=5/4orx=(-5-i*5根号3)/8orx=(-5+i*5根号3)/8
(2)(x-1)^3+216=(x-1+6)*[(x-1)^2-6*(x-1)+36]=(x+5)*(x^2-8x+43)=0
x=-5orx=4+i*3根号3orx=4-i*3根号3