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experimentX
Group Title
For \( a, b, c > 0, abc =1\) show that
\[ \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge a+b+c \]
No Lagrange multiplier allowed.
 one year ago
 one year ago
experimentX Group Title
For \( a, b, c > 0, abc =1\) show that \[ \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge a+b+c \] No Lagrange multiplier allowed.
 one year ago
 one year ago

This Question is Closed

completeidiot Group TitleBest ResponseYou've already chosen the best response.0
\[a^2c+ab^2+bc^2\ge a+b+c\]
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
another form would be it. or \[ \frac{ab^2+bc^2+ca^2}{a+b+c} \ge 1\]
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
most likely this problem won't take more than AMGM
 one year ago

completeidiot Group TitleBest ResponseYou've already chosen the best response.0
i want to say the next step is reducing it to 2 variables but i dont want to think, good luck to the next person
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
here's extra nice problem http://math.stackexchange.com/questions/275208/theleastvalueforfracab354fracbc354fracca354
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
it took nearly week for me to figure out it's solution. try using this technique http://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means#Weighted_AM.E2.80.93GM_inequality it will be lot shorter.
 one year ago
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