Maths questions

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2006-12-18 19:35:01 補充：
1) 4a-2b c = 0 ... (1) 9a-3b c = 0 ... (2)(2)-(1): 5a-b = 05a = ba:b = 1:5 //(1)x1.5: 6a-3b 1.5c = 0 ... (3)(2)-(3): 3a-0.5c = 03a = 0.5ca:c = 0.5:3 //a:b = 1 : 5a: c = 0.5: 3--------------------------------a:b:c = 2.5 : 12.5 : 15

2006-12-18 19:38:00 補充：
由於比例的數不可以以小數表示所以您必須倍大, 再約簡a:b:c = 2.5 : 12.5 : 15 a:b:c = 25 : 125 : 150a:b:c = 1 : 5 : 6 //

2006-12-18 19:48:03 補充：
2) x:a=2:3 and x:b=3:4 and x:c =4:5, then a:b:c=?ｘ：ａ　　　　＝　２：　３ｘ：　　ｂ　　＝　３：　　　４ｘ：　　　　ｃ＝　４：　　　　　５－－－－－－－－－－－－－－－－－－－ｘ：ａ：ｂ：ｃ＝２４：３６：３２：３０ａ：ｂ：ｃ＝３６：３２：３０ａ：ｂ：ｃ＝１８：１６：１５／／

2006-12-18 19:53:25 補充：
3) x y=a and xy=b, then (x-y)²=? (x-y)² = x²-2xy y²= (x y)² - 4xy ----- 會考常出, 一定要識= (a)² - 4(b)= a²-4b //

2006-12-18 19:55:10 補充：
以上 3 題已驗算 !!以上 3 題已驗算 !!以上 3 題已驗算 !!

1. 4a-2b+c=0-----(i)
9a-3b+c=0----(ii)

(ii)-(i): 5a-b =0
5a=b
a:b =1:5

then (b/5)-2b+c=0
9b/5=c
9b=5c
b:c= 5:9

Therefore a:b:c = 1:5:9

2. x:a=2:3 and x:b=3:4 and x:c =4:5
x:a=12:18 and x:b=12:16andx:c=12:15
Therefore, a:b:c = 18:16:15

3. x+y=a and xy=b
(x-y)^2=(x+y)^2-4xy
=a^2-4b

1) If 4a-2b+c=0 and 9a-3b+c=0, then a : b : c = ?

4a - 2b + c = 0 .........(A)
9a - 3b + c = 0 .........(B)

When (B) - (A),
5a - b = 0
b = 5a

When 2x(B) - 3x(A),
(18a - 6b + 2c) - (12a - 6b + 3c) = 0
6a - c = 0
c = 6a

Hence, a : b : c
= a : 5a : 6a
= 1 : 5 : 6.


2) x:a=2:3 and x:b=3:4 and x:c =4:5, then a:b:c=?

x:a = 2:3, then
x/a = 2/3
a = 3x/2

x:b=3:4, then
x/b = 3/4
b = 4x/3

x:c =4:5, then
x/c = 4/5
c = 5x/4

Hence, a : b : c
= 3x/2 : 4x/3 : 5x/4
All times 12/x
= 18 : 16 : 15.


3) x+y=a and xy=b, then (x-y)^2=?

(x-y)^2
= x^2 + y^2 - 2xy
= [(x + y)^2 - 2xy] - 2xy
= (x + y)^2 - 4xy
= a^2 - 4b.

1) 4a-2b+c=0
2b-4a =c

9a-3b+c=0
3b-9a=c

so 3b-9a=2b-4a
b=5a

so 2b-4a=c
c=2(5a)-4a
c=6a

so a : b : c = 1 : 5 : 6

2)x:a=2:3
SO x/a = 2/3
a = (3/2)x

x:b=3:4
so x/b=3/4
b=(4/3)x

x:c=4:5
so x/c=4/5
c=(5/4)x

so a : b : c= 3/2 : 4/3 : 5/4
so = 18 : 16 : 15

3) (x-y)^2 = x^2 - 2xy + y^2

xy=b
x+y=a (x+y)^2 = a^2
(x+y)^2 = x^2 + 2xy + y^2 = a^2

so (x-y)^2 = x^2 - 2xy + y^2
(x-y)^2 = (x^2 - 2xy + y^2) + 2xy -2xy
(x-y)^2 = (x^2 + 2xy + y^2) - 2xy -2xy
(x-y)^2 = (x+y)^2 - 4xy
(x-y)^2 = a^2 -4b

1) If 4a-2b+c=0 and 9a-3b+c=0, then a : b : c = ?
4a-2b+c=0，c=2b-4a
9a-3b+c=0, c=3b-9a
2b-4a=3b-9a
b=5a, c=6a
a : b : c =1:5:6
2) x:a=2:3 and x:b=3:4 and x:c =4:5, then a:b:c=?
x:a=2:3
x/a=2/3
x=(2/3)a
x:b=3:4, x=(3/4)b and x:c =4:5, x=(4/5)c
a:b:c
=(2/3)a=(3/4)b=(4/5)c=k
a=3k/2, b=4k/3, c=5k/4
a:b:c=3/2:4/3:5/4=18:16:15
3) x+y=a and xy=b, then (x-y)^2=?
(x-y)^2
=(x+y)^2-4xy
=a^2-4b