If `a ,b ,a n dc` are positive and `a+b+c=6,` show that `(a+1//b)^2+(b+1//c)^2+(c+1//a)^2geq75//4.`

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove tha ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 a b^2geq4c^3dot

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

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)

Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a=(1-b^3)/b=(1-c^3)/c dot The value of (a^3+b^3+c^3) is _____________.

If a , b , c are consecutive positive integers and (log(1+a c)=2K , then the value of K is logb (b) loga (c) 2 (d) 1

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2