中四數學問題11，唔該快答!!!

1(a) 1/(x+2)+1/(x-2)=2/3
3(x-2+x+2)=2(x+2)(x-2)
3(2x)=2(x^2-4)
3x=x^2-4
x^2-3x-4=0
(x+1)(x-4)=0
x= -1 或 x=4

(b) (x+1)(2-3/x)=4
(x+1)(2x-3)=4x
2x^2-5x+3=0
(2x+1)(x-3)=0
x= -1/2 或 x=3

2(a) x^2-14x+24=0
(x-2)(x-12)=0
x=2 或 x=12

(b) 由(a), y^2+y=0 或 y^2+y=12
y(y+1)=0 或 (y+4)(y-3)=0
y= 0 或 y= -1 或 y= -4 或 y=3
(由小至大排列）y= -4 或 y= -1 或 y= 0 或y=3

3(a) 1-2cos^2x-sinx=0
1-2(1-sin^2x)-sinx=0
2sin^2x-sinx-1=0
(sinx-1)(2sinx+1)=0
sinx=1 或 sinx= -1/2
x=90度 或 x=210度 或x=330度

(b) log(3x+1)+log(x-2)=1 (x>2)
log[(3x+1)(x-2)]=log10
3x^2-5x-2=10
3x^2-5x-12=0
(3x+4)(x-3)=0
x= -4/3(捨去）或 x=3

(c) 2^2x-6(2^x)-16=0
(2^x)^2-6(2^x)-16=0
(2^x+2)(2^x-8)=0
2^x= -2(捨去）或 2^x=8 （因為2^x＞0）
x=3

(d) log5x+log25=3
log[(5x)(25)]=log(10^3)
125x=1000
x=8

1a) 1/x+2 + 1/x-2 = 2/3
2/x = 2/3
x = 3

b) (x+1) (2-3/x) = 4
2x - 3x/x + 2 - 3/x = 4
-3x/x - 3/x + 2x = 2
-3x - 3 + 2x^2 = 2x
2x^2 - 5x - 3 = 0
(2x + 1) (x - 3) = 0
2x + 1 = 0
x = -1/2
or
x - 3 = 0
x = 3

2a) x^2 - 14x + 24 = 0
(x - 12) (x- 2) = 0
x = 2 or 12

b) Since (a), y^2 + y = 0 or y^2 + y = 12
y (y + 1) = 0 or (y + 4) (y - 3) = 0
y = - 4 or y= - 1 or y = 0 or y = 3

3a) 1 - 2cos^2x - sinx = 0
1-2(1-sin^2x)-sinx = 0
2sin^2x-sinx-1= 0
(sinx-1) (2sinx+1) = 0
sinx = 1 or sinx = -1/2
x = 90 o or x = 210 o or x = 330 o

b) log (3x+1) + log (x-2) = 1 , while (x>2)
log[(3x+1)(x-2)] = log10
3x^2-5x-2 = 10
3x^2-5x-12 = 0
(3x+4)(x-3) = 0
x = -4/3 (delete）or x = 3

c) 2^2x-6(2^x) - 16 = 0
(2^x)^2-6(2^x)-16 = 0
(2^x+2)(2^x-8) = 0
2^x = -2 (delete)
or
2^x = 8
x = log8 / log2
x = 3

d) log5x+log25 = 3
log[(5x)(25)] = log(10^3)
125x = 1000
x = 8