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 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

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

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 one A.M., A and two geometric means G_1a n dG_2 inserted between any two positive numbers, show that (G1 ^2)/(G2)+(G2 ^2)/(G_1)=2Adot

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

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 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