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![[Post New]](/templates/default/images/icon_minipost_new.gif) 13 May 2007 12:51:32 IST
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 a1 , a2 , a3 , .................. , an and b1 , b2 , b3 , ........................ ,bn are real no.s then : (a1b1 + a2b2 + ................... + anbn)2 <= (a12 + a22 + ................. an2)(b12 + b22 + ..................... + bn2) Equality holds if : a1/b1 = a2/b2 = ...................... = an/bn a1 , a2 , a3 , .................. , an and b1 , b2 , b3 , ........................ ,bn are real no.s such that : a1 <= a2 <= a3 <= ........................ <= an and b1 <= b2 <= b3 <= .......................... <= bn ; then : n(a1b1 + a2b2 + ..................... + anbn) >= (a1 + a2 + ................... + an)(b1 + b2 + ......................... + bn) x + 1/x >= 2 OR x + 1/x <= -2 ; for x not equal to zero.  ai > 0 ; i = 1 , 2 , 3 , 4 ........................ , n. (a1 + a2 + a3 + .......................... + an)(1/a1 + 1/a2 + 1/a3 + ....................... + 1/an) >= n2
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this article: 16 points
(with 2 
in 5 votes ) [?]
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Moderation Team
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