Question

x^3-6x+4=0怎么解？

Answer 1

解:方程为x³-6x+4=0，化为x³-8-6x+12=0，(x-2)(x²+2x+4)-6(x-2)=0，(x-2)(x²+2x+4-6)=0，(x-2)(x²+2x-2)=0，得:x₁=2，x₂=-1+√3，x₃=-1-√3

Answer 2

f(x)=x^3-6x+4
f(2)=8-12+4=0
x^3-6x+4=(x-2)(x^2+ax-2)
coef. of x
-2-2a=-6
2a=4
a=2
x^3-6x+4
=(x-2)(x^2+2x-2)
x^3-6x+4=0
(x-2)(x^2+2x-2)=0
x=2 or -1+√3 or -1-√3