中四數學...有幾題唔識做啊幫幫手

2007-11-30 3:24 am

1a) 求當x^99+1除以x+1時所得的餘數
b)若今天是星期一,則6^99後將是星期幾?

2a)設f(x)=x^n+2x+3,其中n是一個正奇數 ,求當f(x)除以x+1時所得的餘數
b)利用(a)所得的結果,或其他方法,求當f(x)除以x^2-1時所得的餘數
(b)果題最好用2個方法做比我睇下因為我想識多一個 thx

3a) 證明x^2+x+2x(√x+2)≡(x+(√x+2))^2-2
b)由此,解x^2+x+2x(√x+2)=14

第3題D開方前後既括號係我自己加既方便D睇

有無人幫幫手啊

回答 (1)

Kam Kee

2007-11-30 8:01 am

✔ 最佳答案

1a)
f(x) = x^99+1
f(-1) = (-1)^99 + 1
f(-1) = 0

當x^99+1除以x+1的餘數是 0

b) from (a), sub x = 6
(6^99 + 1) 除 7 的餘數是 0
(6^99) 除 7 的餘數是 6
所以若今天是星期一,則6^99日後將是星期日

2a)
f(x)=x^n+2x+3
f(-1) = (-1)^n + 2(-1) + 3
f(-1) = (-1) -2 + 3
f(-1) = 0

b) x^2-1 = (x+1)(x-1)
利用 (a)
f(-1) = 0
f(1) = 6

let the reminder be ax + b so that
f(x)=x^n+2x+3 = Q(x) * (x^2-1) + ax + b where Q(x) is the quotient
f(1)= a+b = 6 --- (1)
f(-1) = -a +b = 0 --- (2)
solving (1), (2) a = 3, b = 3
therefore the reminder is 3x + 3

3a)
x^2+x+2x(√x+2)
=x^2 + 2x(√x+2)) + x
=x^2 + 2x(√x+2)) + x + (√x+2)^2 - (√x+2)^2
=(x+(√x+2))^2 + x - (√x+2)^2
=(x+(√x+2))^2 + x - (x + 2)
=(x+(√x+2))^2 - 2

b)
x^2+x+2x(√x+2)=14
(x+(√x+2))^2 - 2 = 14
(x+(√x+2))^2 = 16
x+(√x+2) = 4 or -4 (rejected)
x = 2

👍 0 👎 0

中四數學...有幾題唔識做啊 幫幫手

回答 (1)

中四數學...有幾題唔識做啊幫幫手