form4數學

2006-10-27 5:08 am

let f(x)=x^99+k
when f(x) is divided by x+1,the remainder is 1.find the value of k
已搵到k係2,下一條
hence, find the remainder when9^99 is devided by10
點做呀?可唔可以詳細d講解

回答 (1)

用戶9934

2006-10-27 5:15 am

✔ 最佳答案

f(x)=x^99+2=(x+1)q(x)+1

當x=9,

9^99+2=10．N+1 (N是整數)

9^99=10N-1

9^99=10(N-1)+(10-1)

9^99=10(N-1)+9

所以9^99除10後餘數是9

ok^^?

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