if a,b,c are positive real numbers such that

loga/(b-c) = logb/(c-a) = logc/(a-b)

then proove that

1. a(b+c)+ b(c+a) + c(a+b) >= 3
2. a(a)+ b(b) + c(c) >= 3

loga/(b-c) = logb/(c-a) = logc/(a-b) = k (let)(b-c)(loga)/(b-c)^2 = ka^(b-c) = e^(k(b-c)^2)......................(1)Similarly,c^(a-b) = e^(k(a-b)^2)....................(2)b^(c-a) = e^(k(c-a)^2)......................(3)Adding all the eqns. a(b-c)+ b(c-a) + c(a-b) = e^(k(b-c)^2) + e^(k(a-b)^2) + e^(k(c-a)^2) >=3as a,b,c > 0 and are positive real numbers.chec for minimumvalue of a,b,c.i.e a,b,cfor a = b =c =1 it gives 3 minum and for any other no. greater than 1 it will be greater than 3.