F.4 Maths
2013-09-26 6:47 pm
1.There are two positive numbers. One is 8 greater than the other and the sum of their square is 544. Find these two numbers. 2. In the inter-school basketball competition, each team has to play against the other team once. If there are n teams in the competition, the total number of matches M is given by M = n ( n – 1 ) / 2(a) If 10 teams enter the competition, how many matches will be held?(b) If there are 66 matches, how many teams join the competition?(c) If last year’s competition, 65% of the matches were held in a sport centre and the remaining 42 matches were held in schools’ playgrounds. How many teams joined the competition last year?
回答 (2)
2013-09-26 7:56 pm
✔ 最佳答案
(1)Let x be the smaller number
and (x + 8) be the larger number
x^2 + (x + 8)^2 = 544
x^2 + x^2 + 16x + 64 = 544
2x^2 + 16x - 480 = 0
x^2 + 8x - 240 = 0
x = 12 or x = -20 (rejected)
therefore, the two number are 12 and 20.
(2)(a)
M = (10)(10 - 1) / 2 = 45
(2)(b)
n(n - 1) / 2 = 66
n^2 - n = 132
n^2 - n - 132 = 0
n = 13 or n = -12 (rejected)
(2)(c)
total number of matches
= 42 / (1 - 65%)
= 120
n(n - 1) / 2 = 120
n^2 - n = 240
n^2 - n - 240 = 0
n = 16 or n = -15 (rejected)
參考: knowledge
2013-09-28 7:50 pm
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收錄日期: 2021-04-28 14:42:04
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130926000051KK00052