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LsTinyBaby

LsTinyBaby

Đăng ký: 03-10-2012
Offline Đăng nhập: 26-09-2018 - 12:03
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#536650 Tìm min: $$ \frac{x}{2x+3y}+\frac...

Gửi bởi LsTinyBaby trong 08-12-2014 - 00:10

http://www.vnmath.co...ai-hoc-mon.html




#437853 $\frac{1}{a+b}+\frac{1}{b+c...

Gửi bởi LsTinyBaby trong 24-07-2013 - 17:07

Áp dụng Cauchy-Schwarz ta có được \[\frac{1}{{a + b}} + \frac{1}{{b + c}} + \frac{1}{{c + a}} + \frac{1}{{2\sqrt[3]{{abc}}}} = \sum\limits_{cyc} {\frac{{{c^2}}}{{{c^2}\left( {a + b} \right)}}}  + \frac{{{{\left( {\sqrt[3]{{abc}}} \right)}^2}}}{{2abc}} \ge \frac{{{{\left( {c + a + b + \sqrt[3]{{abc}}} \right)}^2}}}{{\sum\limits_{cyc} {{c^2}\left( {a + b} \right)}  + 2abc}} = \frac{{{{\left( {a + b + c + \sqrt[3]{{abc}}} \right)}^2}}}{{\left( {a + b} \right)\left( {b + c} \right)\left( {c + a} \right)}}\]