one `AM` ,`a` and two `GM's` ,` p `and `q` be inserted between any two given numbers then show that `p^3+q^3 =2apq`

If one A.M. A and two G.M.\'s p and q be inserted between two given numbers, shwo that p^2/q+q^2/p=2A

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

If A is the arithmetic mean and p and q be two geometric means between two numbers a and b, then prove that : p^(3)+q^(3)=2pq " A"

If odd number of G.M.\'s are inserted between two given quantities a and b, show that the middle G.M.= sqrt(ab)

If p and q are two prime numbers, then what is their LCM?

If A be one A.M. and p ,q be two G.M. ' s between two numbers, then 2A is equal to (a) (p^3+q^3)/(p q) (b) (p^3-q^3)/(p q) (c) (p^2+q^2)/2 (d) (p q)/2

If p is the first of the n arithmetic means between two numbers and q be the first on n harmonic means between the same numbers. Then, show that q does not lie between p and ((n+1)/(n-1))^2 p.

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that : G^(2)=(2p-q)(2q-p)

If p ,q be two A.M. ' s and G be one G.M. between two numbers, then G^2= a) (2p-q)(p-2q) (b) (2p-q)(2q-p) c) (2p-q)(p+2q) (d) none of these

Let a,b,c are the A.M. between two numbers such that a+b+c=15 and p,q,r be the H.M. between same numbers such that 1/p+1/q+1/r=5/3 , then the numbers are