Question

已知x的三次方减3*x的平方减6x加8=0,求x

已知x的三次方减3*x的平方减6x加8=0,求x

Answer 1

x³-3x²-6x+8=0
x³-x²-2x²+2x-8x+8=0
x²(x-1)-2x(x-1)-8(x-1)=0
(x-1)(x²-2x-8)=0
(x-1)(x-4)(x+2)=0
x=1或x=4或x=-2

Answer 2

x^3-3x^2-6x+8=0
f(x)=x^3-3x^2-6x+8
f(1) =0

x^3-3x^2-6x+8 =(x-1)(x^2+ax-8)
coef. of x
-8-a=-6
a=-2

x^3-3x^2-6x+8 =0
(x-1)(x^2-2x-8)=0
(x-1)(x-4)(x+2)=0
x=1 or 4 or -2