If `a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b)` is always (a)`lt=1/2(a+b+c)` (b)`geq1/3sqrt(a b c)` (c)`lt=1/3(a+b+c)` (d)`geq1/2sqrt(a b c)`

If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always (a) geq12 (b) geq9 (c) lt=12 (d)none of these

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(a c),c+1//(a b) are also in A.P.

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq3//2.

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

If a ,b ,c ,d in R^+ and a ,b ,c,d are in H.P., then (a) a+d > b+c (b) a+b > c+d (c) a+c > b+d (d)none of these

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these