F.4maths續方程

1a) x/[5(x-3)] - 3/[2(x-3)] = x - (1/2)
x/(5x-15) - 3/(2x-6) = x - (1/2)
[(2x^2 - 6x) - (15x - 45)]/(10x^2 - 60x + 90) = x - (1/2)
(2x^2-21x+45)/(10x^2 - 60x + 90) = x - (1/2)
[(2x-15)(x-3)]/[10(x-3)^2] = x - (1/2)
(2x-15)/(10x-30) = (2x-1)/2
4x-30 = 20x^2 - 70x + 30
20x^2 - 74x +60 = 0
x = 5/2 or x=6/5

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

1c) (log x)^2 =1
log x=sqrt(1)
x=10^1
x=10

1d) (log x)^2 -log (x^4) = -4
(log x)^2 - 4 log x + 4 = 0
log x=2(repeated roots)
x=10^2
x=100

1e) (log x)^2 -3 log (x^2) +8 = 0
(log x)^2 -6 log x +8 = 0
log x=4 or log x=2
x=10^4 or x=10^2
x=10000 or x=100

1f) 2^[x(x-4)] =32
(x^2 - 4x) log 2 = log 32
x^2 - 4x = 5
x^2 - 4x - 5 = 0
x=5 or x=-1

1g) 4cosθ-3tanθ=0
4cosθ-3(sinθ/cosθ)=0
[4(cosθ)^2- 3sinθ]/cosθ=0
4(cosθ)^2 -3sinθ=0
4[1-(sinθ)^2] - 3sinθ=0
- 4(sinθ)^2 - 3sinθ + 4 = 0
sinθ=0.693000468 or sinθ=-1.443000468(rejected)
θ=43.87 (correct to 4 sig. fig.)

2a) (cosθ)^2/sin θ=-8/3
[1-(sinθ)^2]/sin θ=-8/3
3-3(sinθ)^2 = -8 sinθ
3(sinθ)^2 - 8sinθ -3=0

2b) 3(sinθ)^2 - 8sinθ -3=0
sinθ=3(rejected) or sinθ=-1/3
θ=-19.5(rejected) or θ=360-19.5
θ=340.5(correct to 1 d.p.)

2014-06-09 22:13:32 補充：
1c) (log x)^2 =1
log x=sqrt(1)
log x=1 or log x=-1
x=10 or x=1/10

2014-06-09 22:19:31 補充：
1g)θ=43.87 or θ=136.13 (correct to 4 sig. fig.)