※ 引述《mack (腦海裡依然記得妳)》之銘言：
: 已知兩正整數 a, b,其算術平均數 A = (a + b)/2,幾何平均數 B = (ab)^(0.5).
: 若 A 與 B 皆為兩位數正整數,且 A 與 B 的十位數及個位數數字恰好相互交換,
: 求 a + b 之值為?
: (請賜教)
A = 10m + n
B = 10n + m
m >= n
11 | A + B
9 | A - B
33 | √[A^2 - B^2]
兩種情況
(1) m =/= n
=> m + n = 11
m - n = 1
=> m = 6, n = 5
=> a + b = 2A = 130
a = 98
b = 32
(2) m = n
=> a = b
A = B = a = 11m
=> a + b = 2A = 22m, m = 1, 2, ..., 9
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.228.135.36
※ 文章網址: http://www.ptt.cc/bbs/Math/M.1419487756.A.10D.html