Suppose a and b are two numbers whose A.M is A. Let `G_1` and `G_2` be two G.M.s between a and b. Prove that `(G_1^2)/(G_2)+(G_2^2)/(G_1)=2A`

Suppose that a and b are two positive numbers so that their difference is 12. If their A.M exceeds their G.M by 2, prove that a+b-2sqrt(ab)=4

If H_(1),H_(2) are two harmonic means between two positive numbers a and b (aneb) , A and G are the arithmetic and geometric means between a and b, then (H_(2)+H_(1))/(H_(2)H_(1)) is

The HM of two numbers is 4. Their AM is A and GM is G. If 2A+G^(2)=27 , then A is equal to

If a , a_(1) , a_(2) ,a_(3) , cdots a_(2n), b are in A.P. and a, g_(1) , g_(2) , g_(3) , cdots , g_(2n), b are in G.P. and h is the H.M of a and b then prove that (a_(1)+a_(2n))/(g_(1)g_(2n))+(a_(2)+a_(2n-1))/(g_(2)g_(2n-1))+cdots+ (a_(n)+a_(n+1))/(g_(n)g_(n+1))=(2n)/(h)

If A and G be the A.M and G.M respectively between two positive numbers, prove that the numbers are A+-sqrt((A+G)(A-G)

If A and G be A. M and G. M respectively between two positive numbers. Prove that the numbers.are A pmsqrt((A+G)(A -G))

Suppose that a group of students consists of 3 boys namely G_1,G_2 and G_3 If two students are selected at random from the group, write the sample space.

Let f and g be two functions defined by f(x)=sqrt(x-1) ,and g(x)=sqrt(4-x^2) .Find f/g