高一 数学 2个一元3次题目 请详细解答,谢谢! (7 8:48:39)

（1） X^3-3X-2= (X^3-X^2)+(X^2-3X-2)
=X^2(X-1)+(X-1)(X-2)=(X-1)(X^2+X-1)=0
X-1=0 或X^2+X-1=0
X1=1, X2=(-1+√5)/2, X3=(-1-√5)/2

(2)x^3-4xy^2-2x^2y+8y^3
=(x^3+8y^3) -(2x^2y+4xy^2)
=(x+2y)(x^2-2xy+4y^2) -2xy(x+2y)
=(x+2y)(x^2-2xy+4y^2-2xy)
=(x+2y)(x-2y)^2

设方程的根为a，b,c.

X^3-3X-2=(x-a)(x-b)(x-c)=x^3-(a+b+c)x^2+(ab+bc+ac)x-abc
a+b+c=0
ab+bc+ac=-3
abc=2
a=2 b=-1 c=-1
X^3-3X-2=(x-2)(x+1)(x+1)

2.x^3-4xy^2-2x^2y+8y^3
=(x^3+8y^3)-2xy(2y+x)
=(x+2y)(x^2-2xy+4y^2)-2xy(x+2y)
=(x+2y)(x^2-4xy+4y^2)
=(x+2y)(x-2y)^2

x^3+1-3(x+1)=0
(x+1)(x^2-x+1)-3(x+1)=0
(x+1)(x^2-x+1-3)=0
(x+1)(x^2-x-2)=0
(x+1)(x+1)(x-2)=0
x=-1,x=2

x^3-4xy^2-2x^2y+8y^3
=(x^3+8y^3) -(2x^2y+4xy^2)
=(x+2y)(x^2-2xy+4y^2) -2xy(x+2y)
=(x+2y)(x^2-2xy+4y^2-2xy)
=(x+2y)(x-2y)^2

1,X^3-3X-2=0
拆 X^3-X-2X-2=0
X(X^2-1) -2(X+1)=0
X(X+1)(