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 gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2 .

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.

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

If a, b, c are all positive, prove that 6abc le bc(b + c) + ca(c + a) + ab(a + b)

If a,b,c are positive unequal real numbers then prove that (bc)/a+(ca)/b+(ab)/cgea+b+c .

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

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

If a, b, c are positive, prove that (a + b + c) (ab + bc + ca) ge 9abc.

If a, b, c are in geometric progression, then show that, (a^(2) + ab + b^(2))/(ab + bc + ca) = (a + b)/(b + c)