 
|
Page 1 of 1
|
[ 7 posts ] |
|
Share: 
|
| Author |
Message |
makar
Posts: 277
Location: India
|
Posted: Sep 13, 2009, 2:42 pm •
# 1
If  are three positive real numbers, prove that  |
|
|
Dimitris X
Posts: 651
Location: Greece
|
Posted: Sep 13, 2009, 2:47 pm •
# 2
makar wrote: If are three positive real numbers, prove that  (nebsit inequality)
_________________
ΠΑΙΡΝΩ ΤΑΜΠΕΛΑ ΚΑΙ ΕΓΩ ΤΟΥ ΕΘΝΙΚΟΥ ΠΡΟΔΟΤΗ ΑΦΙΕΡΩΜΕΝΟ ΚΑΙ ΑΥΤΟ ΣΕ ΚΑΘΕ ΔΟΥΛΟ ΠΑΤΡΙΩΤΗ.....
|
|
|
Evariste-Galois
Posts: 211
|
Posted: Sep 13, 2009, 3:27 pm •
# 3
it's equivalent to
_________________
Mharchi
|
|
|
rachid
Posts: 296
Location: Morocco
|
Posted: Sep 13, 2009, 3:48 pm •
# 4
makar wrote: If are three positive real numbers, prove that The inequality is obviously true because  holds for all positive real numbers  and  . |
|
|
geniusbliss
Posts: 470
Location: chennai,india
|
Posted: Sep 15, 2009, 7:00 am •
# 5
rmo 2006 guys were too lucky!
_________________
Quis custodiet ipsos custodes
Mathematical Dreams 
|
|
|
Zarif
Posts: 38
|
Posted: Dec 31, 2009, 2:16 am •
# 6
This is very easy problem.
| Attachments: |
proof.doc [16 KiB]
Downloaded 54 times
|
|
|
|
zhu rh
Posts: 100
Location: Guangzhou
|
Posted: Dec 31, 2009, 6:34 am •
# 7
That is easily solved by AM-GM and cs
∑(a^2+1)/(b+c)≥∑2a/(b+c)≥∑2a^2/(ab+ac)≥2(∑a)^2/2∑bc≥3
|
|
|
Share:
Moderators: MithsApprentice, N.T.TUAN, Peter, darij grinberg, orl, pbornsztein, Megus, harazi, Arne, pvthuan, blahblahblah, Cezar Lupu, High School Olympiad Moderators
|
|
Page 1 of 1
|
[ 7 posts ] |
|
