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 ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

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 alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of aalpha^2+c//aalpha+b+(abeta^2+c)//(abeta+b) is (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

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

Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

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^(2)+b^(2)+c^(2)=1 where, a,b, cin R , then the maximum value of (4a-3b)^(2) + (5b-4c)^(2)+(3c-5a)^(2) is

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot