Mathematics - Fractions
2009-06-21 9:25 pm
Given 9 / 10 = (1 / A) + (1 / B) + (1 / C) where A, B, C are all distinct integers, find A + B + C.
回答 (1)
2009-06-21 10:29 pm
✔ 最佳答案
Obviously A, B, C all greater than 1. Without loss of generality, assume A < B < C.Since
1/2 + 1/4 + 1/5 = 19/20 <> 9/10
1/2 + 1/4 + 1/6 = 11/12 <> 9/10
1/2 + 1/4 + 1/7 = 25/28 < 9/10
We must have A = 2 and B = 3.
Since 1/2 + 1/3 + 1/15 = 9/10, C = 15
Thus, A + B + C = 2 + 3 + 15 = 20
2009-06-22 01:10:00 補充：
In addition, 1/2 + 1/5 + 1/6 = 13/15 < 9/10
We must have A = 2 and B = 3.
收錄日期: 2021-04-13 16:41:32
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