- #1

- 133

- 5

## Homework Statement

If a,b,c are positive real numbers such that ##{loga}/(b-c) = {logb}/(c-a)={logc}/(a-b)## then prove that

(a) ##a^{b+c} + b^{c+a} + c^{a+b} >= 3##

(b) ##a^a + b^b + c^c >=3##

## Homework Equations

A.M ##>=## G.M

## The Attempt at a Solution

Using the above inequation, I am able to get (b) but I have no idea to do (a) keeping in mind the exponents as a sum whereas in the question the denominators are as a difference.