Re: [中學] 積大和就大
看板Math作者lockheart (Special Thanks to Eason)時間12年前 (2011/08/14 21:10)推噓3(3推 0噓 0→)留言3則, 3人參與討論串4/8 (看更多)
※ 引述《TOMOHISA (YAMASHITA)》之銘言:
: 設a≧b≧c≧d>0,試證:若ad≧bc,則a+d≧b+c。
c≧d implies -d≧-c
with the fact a≧b we can find that
a-d ≧ b-c
Hence (a-d)^2 ≧ (b-c)^2
(a+d)^2 = (a-d)^2 + 4ad ≧ (b-c)^2 + 4bc = (b+c)^2
From the fact that a≧b≧c≧d>0
a+d ≧ b+c
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