中五數學 ,請回答。

1.
(x + 2y) : (3x - y) = 1 : 4
3x - y = 4(x + 2y)
3x - y = 4x + 8y
x = -9y
x/y = -9
x : y = 9 : -1


=====
2.
a : b = 5 : 2 ...... (1)
2a - 3b = 8 ...... (2)

由(1):
a = 5b/2 ...... (3)

把(3)代入(2):
2(5b/2) - 3b = 8
2b = 8
b = 4

把 b= 4 代人(3):
a = 10

所以 a = 10, b = 4


=====
3.
t ∝s/r²
所以 t= ks/r² (k為常數)

當r = 3及s = 6時,t = 2 :
(2) = k(6)/(3)²
k = 3
所以 t= 3s/r²

當t = 36及s = 3時 :
(36) = 3(3)/r²
r² = 1/4
r = 1/2 或 r = -1/2


=====
4.
此題資料不足。（可能打漏題目）


=====
5.
(a)
x² - 7x + 12 = 0
(x - 4)(x - 3) = 0
x = 4 或 x = 3

(b)
6x² - 5x - 6 = 0
(3x + 2)(2x - 3) = 0
x = -2/3 或 x = 3/2

(c)
-5x² + 8x = 1
5x² - 8x + 1 = 0
x = [8 ± √(64 - 4*5*1)]/(2*5)
x = (4 + √11)/5 或 x = (4 - √11)/5

(d)
x(4x - 1) + 3 = 0
4x² - x + 3 = 0
x = [1 ± √(1 - 4*4*3)] / (2*4)
x = [1 ± √(-47)] / 8
此題無實根。


=====
6.
x² + 14x + k =0沒有實根
判別式 Δ < 0
(14)² - 4(1)(k) < 0
4k > 196
k > 49


=====
7.
2x² + 5x + k – 1 = 0有實根
判別式 Δ ≥ 0
(5)² - 4(2)(k - 1) ≥ 0
25 - 8k + 8 ≥ 0
8k ≤ 33
k ≤ 33/8
k的最大值 = 33/8

2011-06-23 02:04:03 補充：
第4題：
y = (k1)x + k2

當x = 2時,y = 1:
1 = (k1)(2) + k2
2(k1) + k2 = 1 ... (1)

當x = 4, y = 7
7 = (k1)4 + k2
4(k1) + k2 = 7 ... (2)

(2) - (1):
2(k1) = 6
k1 = 3

把 k1 = 3 代入 (1):
2(3) + k2 = 1
k2 = -5

y = 3x - 5

當 x = 3:
y = 3(3) - 5
y = 4 ...... 答案