已知x²-x-1=0,(1)求-x³+2x²+2002的值;(2)求x²+x^-2+2014的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 01:55:37
![已知x²-x-1=0,(1)求-x³+2x²+2002的值;(2)求x²+x^-2+2014的值](/uploads/image/z/1271564-44-4.jpg?t=%E5%B7%B2%E7%9F%A5x%26%23178%3B-x-1%3D0%2C%281%29%E6%B1%82-x%26%23179%3B%2B2x%26%23178%3B%2B2002%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82x%26%23178%3B%2Bx%5E-2%2B2014%E7%9A%84%E5%80%BC)
已知x²-x-1=0,(1)求-x³+2x²+2002的值;(2)求x²+x^-2+2014的值
已知x²-x-1=0,(1)求-x³+2x²+2002的值;(2)求x²+x^-2+2014的值
已知x²-x-1=0,(1)求-x³+2x²+2002的值;(2)求x²+x^-2+2014的值
答:
x²-x-1=0
x²=x+1
两边同时除以x:x-1-1/x=0,x-1/x=1
两边平方得:x²-2+1/x²=1,x²+1/x²=3
1)
-x³+2x²+2002
=-(x+1)x+2x²+2002
=x²-x+2002
=1+2002
=2003
2)
x²+1/x²+2014=3+2014=2017