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

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

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

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 and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

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,d are positive numbers such that a,b,c are in A.P. and b,c,d are in H.P., then : (A) ab=cd (B) ac=bd (C) ad=bc (D)none of these

If a, b, c are in HP show that ab + bc = 2ac.