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 one year ago
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
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.

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

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

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

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

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

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1it 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.
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