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

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

If one geometric mean G and two arithmetic means p,q be inserted between two given numbers,then prove that,G^(2)=(2p-q)(2q-p)

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 one A.M.A and tow geometric means G_(1) and G_(2) inserted between any two positive numbers,show that (G_(1)^(1))/(G_(2))+(G_(2)^(2))/(G_(1))=2A

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