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※ 引述《cuttlefish (睡覺真是一種幸福呀~ Ｉ》之銘言：
第四題好像可以用這個不等式:
\
if a 為正實數
sqrt(a)>=2a/(a+1)
\
ps我只會這題啦~
有時間..寫詳細一點好了(我想大家應該早就會了....)
sqrt(a)>=2a/(a+1) 等號成立在 a=0 or 1
sqrt[x/(y+z)]>=2x/(x+y+z)
sqrt[y/(x+z)]>=2y/(x+y+z)
sqrt[z/(x+y)]>=2z/(x+y+z)
相加即可
注意到等號不能全成立
得證
※ 引述《chaogold (dchaodx)》之銘言：
: ※ 引述《myflame (龍隊 紅隊 太陽隊)》之銘言：
: : 感謝chaogold提供題目
: : 1. In triangle ABC prove that a + b + c < r_1 + r_2 + r_3 + min {r_1,r_2,r_3}
: : where r_1 is the exradius opposite a, r_2 is the exradius opposite b and r_3
: : is the exradius opposite c.
: : 2. How can you arrange numbers from 1 to 2003 in a row so that avg. of any
: : two numbers doesn't lie between them? E.g. 2003...1002...1 is invalid as
: : (1+2003)/2=1002
: : 3.Prove that there are infinitely many primes that can be written as the sum
: : of a prime and a power of two.
: : 4. [x/(y+z)]^(1/2) + [y/(x+z)]^(1/2) + [z/(y+x)]^(1/2) > 2
: 第二題學長的解法太妙了！
: 我只能說妙..
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