已知x=100时,ax^2005+bx^2003+cx^2001+5的值为2005,当x=-100时,ax^2005+bx^2003+cx^2001+5的值是多少在线等

Question

已知x=100时,ax^2005+bx^2003+cx^2001+5的值为2005,当x=-100时,ax^2005+bx^2003+cx^2001+5的值是多少
在线等

Answer 1

x=100
ax^2005+bx^2003+cx^2001+5
=a*100^2005+b*100^2003+c*100^2001+5
=2005
所以
a*100^2005+b*100^2003+c*100^2001=2000
x=-100
原式=a*(-100)^2005+b*(-100)^2003+c*(-100)^2001+5
=-a*100^2005-b*100^2003-c*100^2001+5
=-(a*100^2005+b*100^2003+c*100^2001)+5
=-2000+5
=-1995