有條數學題不識計, 請教我

2008-08-22 10:34 pm
Let f(x) = x^99 + k

a) When f(x) is divided by x+1, the remainder is 1. Find the value of k.

這條我識計, 答案是2

但我不識計下面這條.

Hence, find the remainder when 9^99 is divided by 10.

請好心人教我.

回答 (3)

2008-08-22 10:52 pm
✔ 最佳答案
As found from a, k = 2.
So, f ( x ) = ( x + 1 ) Q ( x ) + 1
--> x^99 + 2 = ( x + 1 ) Q ( x ) + 1
Sub x = 9,
9^99 + 2 = ( 9 + 1 ) Q ( 9 ) + 1
9^99 = 10 Q ( 9 ) - 1
9^99 = 10 [ Q ( 9 ) - 1 ] + 9
[ Note: For numeral division, remainder must be non - negative, i.e. >= 0 ]
Hence the remainder is 9.

2008-08-22 16:18:03 補充:
上面個Q ( x )係個quotient,
即係當(x^99 + 2)除以( x + 1 )嗰陣, 個quotient係( x + 1 ), 而remainder係1,
i.e. x^99 + 2 = ( x + 1 ) Q ( x ) + 1

2008-08-22 16:19:26 補充:
舉個例, 9除2等於4餘1, 所以
9 = 2 x 4 + 1

2008-08-28 13:24:50 補充:
如果你仲有問題好歡迎你提出, 但希望你唔好刪咗lee題, 白費我心機!
參考: My Maths Knowledge
2008-09-02 7:37 am
thanks!
2008-08-22 11:04 pm
唔好意思,你第二個STEP我睇唔明白...
點解會係:(X+1)+Q(X)+1
可否解一下, 謝謝!


收錄日期: 2021-04-25 23:23:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080822000051KK00609

檢視 Wayback Machine 備份