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![[Post New]](/templates/default/images/icon_minipost_new.gif) 14 Mar 2008 14:06:34 IST
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Time wounds all heels |
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14 Mar 2008 18:13:36 IST
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i am assuming that  are positive
consider any point  from there draw rays  and  such that  and 
bisect the angle and draw  .
now the given inequality reduces to the triangle inequality
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14 Mar 2008 18:15:09 IST
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EDITED!
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14 Mar 2008 18:55:44 IST
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You chaps from AOPS are downright ruffians. good job fellas!
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Time wounds all heels |
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14 Mar 2008 19:25:22 IST
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(a2+b2)/2 >= ab => ab<=(a2+b2)/2  (a 2-ab+b 2) >= (a 2 -(a 2+b 2)/2 +b 2) = ((a 2+b 2)/2) similarly (b 2-bc+c 2) >= ((b 2+c 2)/2) using AM of mth power >= mth power of AM ( ((a 2+b 2)/2) + ((b 2+c 2)/2))/2 > = [((a 2+b 2)/2)+(b 2+c 2)/2) /2 ] 1/2which is = (a 2+b 2+b 2+c 2) ...now i think that rearrangement inequality can be employed to prove the final answer ... |
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14 Mar 2008 19:30:09 IST
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why are we ruffians sir? Becos we attack all problems?  ..
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14 Mar 2008 19:34:46 IST
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ruffian
noun
1. A rough, violent person who engages in destructive actions
just to add
those destructive actions are done on problems!!
 
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Impossible To be Impossible is Impossible |
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14 Mar 2008 19:41:09 IST
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marauders is more like it
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Time wounds all heels |
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