If `a,b,c` are unequal and positive then show that `(bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)`

Statement 1 If a,b,c are three positive numbers in GP, then ((a+b+c)/(3))((3abc)/(ab+bc+ca))=(abc)^((2)/(3)) . Statement 2 (AM)(HM)=(GM)^(2) is true for positive numbers.

If a,b,c are in H.P and ab+bc+ca=15 then ca=

The value of (bc)^log(b/c)*(ca)^log(c/a)*(ab)^log(a/b) is

If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)]^(1/2)+tan^(-1)[(b(a+b+c))/(ca)]^(1/2)+tan^(-1)[(c(a+b+c))/(ab)]^(1/2) , then tantheta equals

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

If a , b , c are all non-zero and a+b+c=0 , then (a^(2))/(bc)+(b^(2))/(ca)+(c^(2))/(ab)= ? .

If a,b,c are in A.P. prove that the following are also in A.P. (a(b+c))/(bc) , (b(c+a))/(ca) , (c(a+b))/(ab)

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)" are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)" are also in A.P."