中4簡單數學問題?急(唔洗列式)

1.若 f(x+1)=x^2-2x,求f(3)

f(3)=2^2-2(2)=0


2.若 f(x)=x/x+1,其中 x≠1，則　f(1/x-1)=?
f(1/(x-1))
=[1/(x-1)]/[1/(x-1)+1]
=[1/(x-1)]/[x/(x-1)]
=1/x


3.16a/8b=2a/b


4.若 3(2^x-3)+1=25,則x=?
3(2^x-3)+1=25
3(2^x-3)=24
(2^x-3)=8
2^x=11
x=log11/log2

5.己知 x^1/2+x^-1/2=3,求 x^2+1/x^2的值
x^1/2+x^-1/2=3
(x^1/2+x^-1/2)^2=9
x+2+1/x=9
(x+1/x)=7
x^2+1/x^2=49-2=47

6. (x^3 y^-6)^1/3 (x^3/2 y^-1)^-2=?
(x^3 y^-6)^1/3 (x^3/2 y^-1)^-2
=(x y^-2) (x^-3 y^2)
=(x^4)(y^-4)
=(x/y)^4

7.若x-3是ax^2 + bx - 6的因式,則3a+b+5=?
令f(x)=ax^2 + bx - 6
f(3)=0
9a+3b-6=0
3a+b=2
3a+b+5=7

8.若x^2+2x-5≡ a(x-1)^2 + b(x^2-2),則 a和 b=?
x^2+2x-5≡ a(x-1)^2 + b(x^2-2)
代x=sqrt(2)
2+2sqrt(2)-5≡ a(sqrt(2)-1)^2
a=[2sqrt(2)-3]/[3-2sqrt(2)]
a=-1

代x=1,-b=-2,b=2

9.解方程2x^2/3 - 5x^1/3 - 3=0
令y=x^(1/3)
2y^2-5y-3=0
(y-3)(2y+1)=0
y=3 or y=-1/2
x=y^3=>x=27 or -1/8

1...代x=4
2....1/x
3...2(a/b)
4... 6
5....47
6.....(x/y)^4
7....7
8...a=-1 b=2
9.....x=9 or -1/8

2009-02-05 22:35:53 補充：
sorry...
1...代x=2...=0