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)

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

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 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 ,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

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"

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)

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

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.

Show that if A and G .are A.M. and G.M. between two positive numbers , then the numbers are A+- sqrt(A^(2) -G^(2))