已知|x|=3x+1,则(64x2+48x+9)2005=_.

问题描述:

已知|x|=3x+1,则(64x2+48x+9)2005=______.

|x|=3x+1,
x=3x+1或x=-3x-1,
解得x=-

1
2
或x=-
1
4

(64x2+48x+9)2005
=[(8x+3)2]2005
=(8x+3)5000
x=-
1
2
时,(8x+3) 5000=[8×(−
1
2
)+3]5000
=1;
x=-
1
4
时,(8x+3) 5000=[8×(−
1
4
)+3]5000
=1.
故答案为:1.