Maths~~~ F.2~~~~~急

1.
(x + 1)(x - 1) + (1 - x) / 3
= (x - 1)(x + 1 - 1/3)
= (x - 1)(x + 2/3)

2.
x + y = 6
x = 6 - y

x^2 - y^2 = 9
(6 - y)^2 - y^2 = 9
36 -12y + y^2 - y^2 = 9
27 = 12y
y = 9/4
x = 15/4

3.
don't know what is the question
i guess the question is
u = t / (t + d)

when u = -1/3 & t = 3
-1/3 = 3 / (3 + d)
-3 - d = 9
d = -12

4.
p(x + q) = qx - p
px + pq = qx - p
px - qx = -p - pq
x(p - q) = -p - pq
x = (-p - pq) / (p - q)

5.
S = (2n - 4) x 90
S / 90 = 2n - 4
S / 90 + 4 = 2n
n = S / 180 + 2

6.
2x - 3y - 55 = 0 ... (1)
3x + 2y - 271 = 0 ... (2)

2 (1) + 3 (2):
4x - 110 + 9x - 813 = 0
9.3x = 923
x = 71

2(71) - 3y - 55 = 0
3y = 87
y = 29

7.
0.5x + 1.3y - 10 = 0 ... (1)
7x - 3y + 7 = 0 ... (2)

14 (1) - (2):
18.2y - 140 - 3y + 7 = 0
15.2y = 133
y = 8.75

7x - 3(8.75) + 7 = 0
7x = 19.25
x = 2.75

8.
10x = 8(x + 1)
10x = 8x + 8
2x = 8
x = 4

1)
(x + 1)(x - 1) + (1 - x)/3
= (x + 1)(x - 1) - (1 / 3)(x - 1) (留意：減數、被減數交換，要加負號)
= [(x + 1) - 1/3] (x - 1)
= (x + 2/3)(x - 1)

2)
┌ x + y = 6 ------- (1)
┤
└ x² - y² = 9 ------- (2)
From (2), x² - y² = (x + y)(x - y) = 9 ------ (3)
Sub (1) into (3),  (6)(x - y) = 9
  x - y = 3 / 2 ----- (4)
(1) + (4): 2x = 6 + 3 / 2 = 15 / 2
x = 15 / 4 ----- (5)
Sub (5) into (1),￮￮ 15 / 4 + y = 6, y = 9 / 4
∴ x = 15 / 4, and y = 9 / 4

3)
t
Is that u = ------ ?
 t + d

Put u = -1 / 3, t = 3, we have
3
- 1/3 = --------
3 + d
-1 - (1/3)d = 3
- (1/3)d = 4
d = -12

4)
p(x + q) = qx - p
px + pq = qx - p
px - qx = - p - pq
(p - q)x = - p(1 + q)
 p(1 + q)
x = ---------------
p - q

5)
S = (2n - 4) x 90
 S
2n - 4 = ----
90
S
2n = ---- + 4
90
S
∴ n = ----- + 2
 180

6)
┌ 2x - 3y - 55 = 0--- (1)
┤
└ 3x + 2y - 271 = 0 --- (2)
2 x (1) + 3 x (2):13x = 923
x = 71---- (3)
Sub (3) into (1),2(71) - 3y = 55
 y = 29
∴ x = 71 and y = 29

7)
┌ 0.5x +1.3y - 10.1 = 0--- (1)
┤
└  7x - 3y + 7 = 0--- (2)
3 x (1) + 1.3 x (2):10.6x = - 21.2
x = 2---- (3)
Sub (3) into (2),7(2) - 3y + 7 = 0
 y = 7
∴ x = 2 and y = 7

8)
Assume productivity is proportional to the number of people x
(如果您將來讀經濟的話，上述的假設你會知道在實際情況是錯的。但現在你是 F. 2，這個假定是對的。)
10x = 8(x + 1) (同一個工作量, same workload)
10x - 8x = 8
2x = 8
∴ x = 4