- #1
erisedk
- 374
- 7
Homework Statement
If a+b+c=0 then ( (b-c)/a + (c-a)/b + (a-b)/c )( a/(b-c) + b/(c-a) + c/(a-b) ) is equal to:
Ans: 9
Homework Equations
AM>=GM>=HM
Equality holds when all numbers are equal.
The Attempt at a Solution
I tried using AM>=GM.
( (b-c)/a + (c-a)/b + (a-b)/c + a/(b-c) + b/(c-a) + c/(a-b) )/6 >= 1
The AM side doesn't seem to simplify. All the numbers on the GM side cancel leaving me with one. I know I need to convert it into some form of a+b+c=0 but can't figure out how.