Suppose that F,G and Q are polynomials and
F(x) / Q(x) = G(x) / Q(x)
for all x except when Q(x)=0, Prove that F(x) = G(x) for all x
煩請各位大大指教,感謝
微積分證明一問
2010-02-28 5:07 am
回答 (2)
2010-02-28 12:34 pm
✔ 最佳答案
設Q(x)=0有n個根:a1,a2,…,an1.x >< ak(k=1~n),F(x)/ Q(x)=G(x)/ Q(x),=> F(x)=G(x)
2.x= ak(k=1~n), F(ak)=(x-> ak )lim F(x)……….F(x)連續函數
= (x-> ak )lim [F(x)* Q(x)]/ Q(x)
= (x-> ak )lim [G(x)* Q(x)]/ Q(x)
= (x-> ak )lim G(x)
= G(ak) ……….G(x)連續函數
由1.2.對所有的x, F(x)=G(x)
2010-03-01 10:45 pm
多項式F(x)-G(x)=0有無限多個根(總會超過deg(F(x)-G(x))),
so, F(x)-G(x)為零多項式, ie. F(x)=G(x) for all x.
so, F(x)-G(x)為零多項式, ie. F(x)=G(x) for all x.
收錄日期: 2021-04-30 14:22:51
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100227000015KK09904