a : b = 2 : 1 and b : c = 3 : 5, where a, b and c are positive numbers.
(a) Find a : b : c；
(b) If ab + bc + ca =252, find the values of a, b and c.
maths question
2007-06-27 5:23 am
回答 (3)
2007-06-27 5:28 am
✔ 最佳答案
a) 6:3:5b) let a = 6x, b =3x, c=5x
18x^2 +15x^2 + 30x^2 = 252
63x^2 = 252
x^2=4
x= 2 (not -2, since a, b, and c are positive numbers)
then a = 12, b = 6, c = 10
參考: 自己
2007-06-28 12:30 am
a :b =2:1
b:c = 3:5
--------------------
a :b:c =6: 3:5
Let a=6k,b=3k and c=5k.
ab + bc + ca = 252
(6k)(3k) + (3k)(5k) + (5k)(6k) = 252
18k² + 15k² + 30k² = 252
k²(18+15+30)=252
63k² = 252
k²=4
k=2 or k= -2 (rejected)
a=6k=6(2)=12 ,b=3k=3(2)=6 ,c=5k=5(2)=10
a=12, b=6 ,c=10
b:c = 3:5
--------------------
a :b:c =6: 3:5
Let a=6k,b=3k and c=5k.
ab + bc + ca = 252
(6k)(3k) + (3k)(5k) + (5k)(6k) = 252
18k² + 15k² + 30k² = 252
k²(18+15+30)=252
63k² = 252
k²=4
k=2 or k= -2 (rejected)
a=6k=6(2)=12 ,b=3k=3(2)=6 ,c=5k=5(2)=10
a=12, b=6 ,c=10
2007-06-27 6:26 am
a)
a:b = 2:1, ie. a/b = 2/1
2b = a
b:c = 3:5
bcoz 2b = a, (1/2a)/c = 3/5
a/c = 6/5
ie. a:c = 6:5
a:b:c = 6:3:5
b) let a = 6k, b = 3k, c = 5k
6k*3k + 3k*5k + 5k*6k = 252
18k^2 + 15k^2 + 30k^2 = 252
63k^2 = 252
k^2 = 4
k = 2
a = 12, b = 6 & c = 10
a:b = 2:1, ie. a/b = 2/1
2b = a
b:c = 3:5
bcoz 2b = a, (1/2a)/c = 3/5
a/c = 6/5
ie. a:c = 6:5
a:b:c = 6:3:5
b) let a = 6k, b = 3k, c = 5k
6k*3k + 3k*5k + 5k*6k = 252
18k^2 + 15k^2 + 30k^2 = 252
63k^2 = 252
k^2 = 4
k = 2
a = 12, b = 6 & c = 10
收錄日期: 2021-04-12 20:00:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070626000051KK04364