F.4 maths~11題(20分)

👨🏻‍🏫 學術台數學

wing yin

2010-01-06 11:02 pm

1) 若和 α和α-2 是二次方程 3x^2+8x+m=0 的根, 求α 和m 的值。

2)若α和 4α 是二次方程 9x^2-kx+4=0 的根 , 其中 k > 0 , 求 α和 k 的值。

3)已知 f (x) = (x+2) (x-2) + ax +b。若f (2) = 2 及f (-2)=4 , 求a 和b 的值。

4)設f (x) = 3x-1 及 g (x) = x-2。
(a) 若f (2x) = g (3x) ,求 x 的值。
(b) 若H (x) =3 f (x)+ 2 g (x) 及 H(a)=5 , 求 a 的值。

5) m^1/4 n^2/3 ÷ ( 2m^2/3 n)^ -2 ÷ (27/√m)^ -1/3

6) 4√x^3 - 500 =0

解以下聯立方程

7)
5^ x+2y =125
25^ 2x+y =1

8)
4^ 3x-y = 4√256
(3/2)^ x+y = 8/27

9)
2^ 3x = 4^ y+1
5^ x-2 =5^ 2-y

10)
3^ 2x-1 -3^ 5-y =0
9^x -3 (81y) =0

11)
4^ x ●16^ y = 128
(√5)^x = 25^y-1

更新1:

回答 (2)

用戶19657

2010-01-07 6:51 am

✔ 最佳答案

1)sum ofroot: (alpha-2)+(alpha)=-8/3
alpha=-1/3
product of root: alpha(alpha-2)=m/3
m=7/3

2)can't understand

3) f(2) =a(2) + b = 2 ...[1]
f(-2) = a(-2) + b = 4 ...[2]

[1]+[2]=2b=6=> b=3
sub b=3into [1], a=-1/2

4)
(a) f(2x) = 3(2x)-1 = 6x - 1
g(3x) = 3x - 2
6x -1 = 3x - 2
3x = -1
x = -1/3

(b) 5=3f(a)+2g(a)
=9a-3+2a-4
=11a-7
.'. 5+7=11a
a=12/11

5 and 6) can't read the questions
7)是這樣嗎?
(5^ x)+2y =125
(25^ 2x)+y =1
如是, (5^ x)=125-2y
sub (5^ x) into [2], (125-2y)^4 +y=1
use binomial

8-11) also can't understand as the index is not shown clearly, and the symbols are messy..

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MagicHand

2010-01-07 3:46 am

3) f(2) = (2+2) (2-2) + a(2) + b = 2 ...[1]
f(-2) = (-2+2) ( -2-2) + a(-2) + b = 4 ...[2]

(4)(0) + 2a + b = 2
2a + b = 2 ...[3]
(0)(-4) - 2a + b = -4
-2a + b = -4 ...[4]

[4] - [3] :
(-2a + b) - (2a+b) = -4 - 2
-2a + b - 2a - b = -6
-4a = -6
a = 3/2
From [3]:
2a + b = 2
3/2 + b = 2
b = 1/2

4)
(a) f(2x) = 3(2x)-1 = 6x - 1
g(3x) = 3x - 2
6x -1 = 3x - 2
3x = 1
x = 1/3

(b) 3f(x) = 9x-3 ... 2g(x) = 2x-4
H(x) = 9x-3+2x-4
= 11x - 7
H (a) = 11a - 7 = 5
11a=12
a=12/11

P.S.
只係幫到甘多
1,2,5,6 ,11 亂碼睇吾明
7,8,9,10 次方睇吾明
sorry

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