中科新闻网合肥网络推广mdseo:初一数学
来源：百度文库 编辑：中科新闻网 时间：2024/04/28 13:44:12
X的4次方-X的3次方-7倍的X的平方+X+6=O
x^4-x^3-7x^2+x+6=0
x^4-x^2-x^3-6x^2+x+6=0
x^2(x^2-1)-x^2(x+6)+(x+6)=0
x^2(x^2-1)-(x+6)(x^2-1)=0
(x^2-1)(x^2-x-6)=0
(x-1)(x+1)(x+2)(x-3)=0
所以x1＝1,x2＝-1，x3＝3,x4=-2
x^4-x^3-7x^2+x+6
=x^4-x^3-6x^2-x^2+x+6
=x^2(x^2-x-6)-(x^2-x-6)
=(x^2-1)(x^2-x-6)
=(x-1)(x+1)(x-3)(x+2)=0
所以x1＝1,x2＝-1，x3＝3,x4=-2
x^4-x^3-7x^2+x+6=0
x^4-x^2-x^3-6x^2+x+6=0
x^2(x^2-1)-x^2(x+6)+(x+6)=0
x^2(x^2-1)-(x+6)(x^2-1)=0
(x^2-1)(x^2-x-6)=0
(x-1)(x+1)(x+2)(x-3)=0
所以x1＝1,x2＝-1，x3＝3,x4=-2
分解因式法:
x^4-x^3-7x^2+x+6=0
x^4-x^2-x^3-6x^2+x+6=0
x^2(x^2-1)-x^2(x+6)+(x+6)=0
x^2(x^2-1)-(x+6)(x^2-1)=0
(x^2-1)(x^2-x-6)=0
(x-1)(x+1)(x+2)(x-3)=0
所以x1＝1,x2＝-1，x3＝3,x4=-2
因式分解得
(x+2)(x+1)(x-1)(x-3)=0
x=-2或x=-1或x=1或x=3
x^4-x^3-7x^2+x+6
=x^4-x^3-6x^2-x^2+x+6
=x^2(x^2-x-6)-(x^2-x-6)
=(x^2-1)(x^2-x-6)
=(x-1)(x+1)(x-3)(x+2)=0
所以x1＝1,x2＝-1，x3＝3,x4=-2