[急]八年级数学题

显示全部楼层 · 2008-12-30 21:01:00

(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+1
答案是x^64，可过程怎么算？？？
[^是乘方的意思。]

千问 · 2008-12-30 21:01:00

是不是先乘以(x-1)再除以(x-1)？(x-1)[(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+1]/(x-1)=[(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+x-1]/(x-1)=[(x^4-1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+x-1]/(x-1)=[(x^8-1)(x^8+1)(x^16+1)(x^32+1)+x-1]/(x-1)=[(x^16-1)(x^16+1)(x^32+1)+x-1]/(x-1)=[(x^32-1)(x^32+1)+x-1]/(x-1)=(x^64-1+x-1)/(x-1)……...

千问 · 2008-12-30 21:01:00

设(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+1 =A 等式两边同乘(x-1),利用公式(A-B)(A+B)=A^2-B^2 X^64+X-2=A(X-1) 解得A,跟你的答案不一样...

千问 · 2008-12-30 21:01:00

不要相信现在的印刷，题或者答案肯定有一个错了，我照题作吧。(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)+1 ＝[（x-1）(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)／（x-1）]+1＝[（x2-1）)(x^2+1)(x^4+1)(x^8+1)(x^16+1...