已知x2+x+3=0，求x5+3x4+2x3+2x2-10x的值
答案:1 悬赏:80 手机版
解决时间 2021-04-06 07:48
- 提问者网友：雪舞兮
- 2021-04-05 08:41
已知x2+x+3=0，求x5+3x4+2x3+2x2-10x的值
最佳答案
- 五星知识达人网友：持酒劝斜阳
- 2021-04-05 10:08
∵x2+x+3=0，
∴x2+x=-3，
x5+3x4+2x3+2x2-10x
=x3（x2+x）+2x4+2x3+2x2-10x
=-3x3+2x4+2x3+2x2-10x
=2x4-x3+2x2-10x
=2x2（x2+x）-3x3+2x2-10x
=-3x3-4x2-10x
=-3x（x2+x）-x2-10x
=9x-x2-10x
=-x2-x
=-（x2+x）
=3．
∴x2+x=-3，
x5+3x4+2x3+2x2-10x
=x3（x2+x）+2x4+2x3+2x2-10x
=-3x3+2x4+2x3+2x2-10x
=2x4-x3+2x2-10x
=2x2（x2+x）-3x3+2x2-10x
=-3x3-4x2-10x
=-3x（x2+x）-x2-10x
=9x-x2-10x
=-x2-x
=-（x2+x）
=3．
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