concerning sequences!

2007-05-26 8:57 pm
concerning sequences!

36.(a)If the arithmetic mean of two numbers is p and their geometric mean is q ,
find the two numbers in terms of p and q.
(b)If p =30 and q=18 , findthe values of the two numbers in (a).

answers:(a)p+√p^2-q^2 , p-√p^2-q^2
(b)54,6

How can find that??

回答 (1)

2007-05-26 9:15 pm
✔ 最佳答案
Let a, b be the two numbers

For (a),

a + b = 2p .......................... (1)

√ab = q
ab = q^2
a = q^2 / b .......................... (2)

Put (2) into (1),
q^2 / b + b = 2p
q^2 + b^2 = 2bp
b^2 - 2bp + q^2 = 0

b = [ p +/- √(4p^2 - 4q^2) ] / 2 = p +/- √(p^2 - q^2)

Note that a and b are symmetric, hence the answer.

For (b), simply put p=30 and q=18 into the answer of (a).


收錄日期: 2021-04-12 19:43:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070526000051KK01683

檢視 Wayback Machine 備份