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)`

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

For positive numbers a,b c,show that (bc)/(a)+(ac)/(b)+(ab)/(c)>=a+b+c

If a,b,c are distinct positive real numbers then (bc)/(a)+(ca)/(b)+(ab)/(c) is greater than or equal

Factorise bc(b-c)+ca(c-a)+ab(a-b)

If a,b,c are in A.P., then (bc)/(ca+ab),(ca)/(bc+ab),(ab)/(bc+ca)

If a,b,c are in Ap, show that (i) (b +c-a),(c+a-b) ,(a+b-c) are in AP. (bc -a^(2)) , (ca - b^(2)), (ab -c^(2)) are in AP.

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

If a,b,c are in G.P.then prove that (a^(2)+ab+b^(2))/(bc+ca+ab)=(b+a)/(c+b)

If a, b, c all positive and not euqal, then the value of ((a+b+c)(ab+bc+ca))/(abc) is :