幫幫我!!

f(x) = x^2-x+1
f(x+1) = (x+1)^2-(x+1)+1
= x^2+x+1
f(x+1) - f(x) = 2x

y = 2x^2-4x+c 的圖像通過點(1,k)
k = 2(1)^2-4(1)+c
= 2-4+c = c-2

方程4x^2+kx+9=0有相等的正根
delta = 0
ie. k^2-4(4)(9)=0
k^2 = 144
k = 12 or k = -12

x(x-6)=x
x^2-6x=x
x^2-7x=0
x(x-7)=0
x = 0 or x = 7

pq+2q=10 --- (1)
4p+q=14 --- (2)
From (2), p = (14-q)/4
Therefore,
(14-q)/4 * q + 2q = 10
(14-q)q + 8q = 40
22q-q^2-40=0
(q-20)(q-2)=0
q = 20 or q = 2

f(x)=2x^2-3x+4
f(1)=2(1)^2-3(1)+4=3
f(-1)=2(-1)^2-3(-1)+4=9
f(1)-f(-1) = 3-9 = -6

B=a^2-3 --- (1)
B=4a-3 --- (2)
From (2), a = (B+3)/4
Therefore, B= [(B+3)/4]^2-3
16B=B^2+6B+9-48
B^2-10B-39=0
(B-13)(B+3)=0
B = 13 or B = -3

二次方程kx^2+6x+(6-k)=0 有等根
6^2-4k(6-k)=0
36+4k^2-24k=0
(k-3)^2=0
k = 3

x^2+2ax+8
=x^2-2ax+a^2+8-a^2-4ax
=(x-a)^2+8-4ax-a^2

Therefore, b = 8-4ax-a^2

若f(x)= x 1
_____ ,則f(3)f(__)=??
1+x 3

這題不太明白，可否check清楚？

3x^2=21x
3x^2-21x=0
3x(x-7)=0
x = 0 or x = 7

2006-10-17 23:28:39 補充：
f(x) = x/(1+x)f(3) = 3(1+3) = 3/4f(1/3)= (1/3) / (1 + 1/3)= 1/4Therefore, f(3)f(1/3) = (3/4)(1/4)= 3/16