A community for students.
Here's the question you clicked on:
 0 viewing
experimentX
 3 years 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.
experimentX
 3 years 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.

This Question is Closed

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

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

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

experimentX
 3 years 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.