→ wayn2008 :w^5=1,1+w+w^2+w^3+w^4=0 05/09 13:26
→ sugar317 :我現在不懂1+w+w^2+w^3+w^4=0 怎來的 05/09 13:32
→ wayn2008 :w^5-1=0=>(w-1)(1+w+w^2+w^3+w^4)=0=>因為w不等於1 05/09 13:36
→ wayn2008 :所以後面這串等於0 05/09 13:36
→ sugar317 :了解 我大概看懂了 所以後面就利用這兩條件 05/09 13:39
→ sugar317 :就可以解出來了 05/09 13:39
→ sugar317 :感恩 05/09 13:46
→ wayn2008 :2.(2+w)(2+w^2)(2+w^3)(2+w^4) 05/09 13:49
→ wayn2008 :w為x^5=1的根=>(x-1)(x-w)(x-w^2)(x-w^3)(x-w^4)=0 05/09 13:50
→ wayn2008 :(x-1)(x-w)(x-w^2)(x-w^3)(x-w^4)=(x-1)(x^4+x+..+1) 05/09 13:52
→ wayn2008 :(x-w)(x-w^2)(x-w^3)(x-w^4)=(x^4+x+..+1) x=-2 05/09 13:52
→ sugar317 :其實我第2小題有點不解(x-w)...變成(-2-w)... 05/09 14:06
→ sugar317 :原式應該是(2+w)(2+w^2)(2+w^3)(2+w^4) 05/09 14:07
→ sugar317 :他*-號沒差嗎 05/09 14:08
→ wxtab019 :4個都有負號阿 05/09 14:12
→ wayn2008 :(-2-w)(-2-w^2)(-2-w^3)(-2-w^4)=(-2)^4...提出來 05/09 14:14
→ sugar317 :對耶 不好意思 眼殘....感謝囉 05/09 14:16