※ 引述《GuanSi (冠希)》之銘言：
: 2.a,b,c為互不相等的正整數
: a,b,c的倒數和為13/210
: 求a+b+c最小值
If a,b,c are real
then (a+b+c)(1/a+1/b+1/c) >= (1+1+1)^2
(a+b+c) >= 9*210/13 = 145.38...
min(a+b+c) occurs at a=b=c=3*210/13=630/13
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Consider 630=2*3^2*5*7
If a,b,c are integers
we assume a=630/h, b=630/k, c=630/q
then h+k+q=39
we assume a<b<c, then 3/a > 13/210, a<630/13 and 1/a<13/210, a>630/39
possible h is 14,15,18,21,30,35
(i) h=14
a=630/14, b=630/(12-r), c=630/(13+r)
when r=2 , b,c are integers
a=45, b=630/10=63, c=630/15=42
a+b+c=150
actually, 150 is the minimum.
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◆ From: 123.194.224.241
※ 編輯: JohnMash 來自: 123.194.224.241 (05/22 03:36)